When is it optimal to delegate: The theory of fast-track
authority∗
Levent Celik†
Bilgehan Karabay‡
John McLaren§
March 16, 2012
Abstract
With fast-track authority (FTA), the US Congress delegates trade-policy authority
to the President by committing not to amend a trade agreement. Why would it cede
such power? We suggest an interpretation in which Congress uses FTA to forestall
destructive competition between its members for protectionist rents. In our model: (i)
FTA is never granted if an industry operates in the majority of districts; (ii) The more
symmetric the industrial pattern, the more likely is FTA, since competition for protectionist rents is most punishing when bargaining power is symmetrically distributed;
(iii) Widely disparate initial tariffs prevent free trade even with FTA.
Keywords: Fast-track authority; Trade Policy; Multilateral Legislative Bargaining;
Political Economy; Distributive Politics.
JEL classification: C72, C78, D72, F13.
∗
We would like to thank to seminar participants at the University of Colorado-Boulder, the University
of Adelaide, the University of Southern Australia, and Auckland University of Technology, as well as participants at the ASSET annual meetings in 2009. We are also grateful to CERGE-EI, the University of
Virginia and the University of Auckland for their hospitality during the authors’ visits. This research was
supported by a grant (project reference number 3625352/9554) from the University of Auckland Faculty
Research Development Fund. All opinions expressed are those of the authors and have not been endorsed
by the University of Auckland. All errors are our own.
†
CERGE-EI (a joint workplace of the Center for Economic Research and Graduate Education, Charles
University, and the Economics Institute of the Academy of Sciences of the Czech Republic), Politickych
veznu 7, 111 21, Prague 1, Czech Republic. E-mail: [email protected]. URL: http://home.cerge-ei.cz/celik.
‡
Department of Economics, University of Auckland, Owen G. Glenn Building, 12 Grafton Road, Auckland
1010, New Zealand. E-mail: [email protected]. URL: http://bilgehan.karabay.googlepages.com.
§
Department of Economics, University of Virginia, P.O. Box 400182, Charlottesville, VA 22904-4182.
E-mail: [email protected]. URL: http://people.virginia.edu/˜jem6x.
1
Introduction
A peculiar, but crucial, institution of trade policy in the United States is a legislative device known as Fast Track Authority (FTA).1 This is a temporary authority that Congress
sometimes gives to the President at its discretion, and which empowers the President to
negotiate a trade agreement under conditions that allow for rapid ratification with a Congressional commitment to vote up or down with – importantly – no amendments permitted.
In practice, it is a matter of consensus that FTA is a precondition for US participation in
trade negotiations with foreign governments, but it is a paradoxical institution because it is
a voluntary cessation of some of Congress’ own power to the President.
In this paper we attempt to explain Congress’ motivation in adopting FTA. We use some
insights from the political economy of public finance to show that Congressional amendments
of a trade agreement can result in a sort of ruinous competition as each member of Congress
seeks advantage for his constituents, making constituents in all districts worse off in the
process. One motivation for a measure like FTA can be to avoid this problem by effectively
delegating trade policy to the executive branch.
This argument is similar to observations made by some close observers of US trade policy
history, such as Koh (1992, p. 148), who suggests that one of the principal reasons Congress
wanted FTA is that “it controlled domestic special interest group pressures that might otherwise have provoked extensive, ad hoc amendment of a negotiated trade accord.” Destler
(1991) argues that the disaster of the Smoot-Hawley tariff of 1930 had motivated Congress
to delegate trade policy largely to the executive branch, avoiding the sometimes ‘chaotic’
process of Congressional amendments (p. 263) and allowing for more liberal outcomes than
Congress itself would have adopted on its own (pp. 264-5). He emphasizes that this delegation of authority (through FTA and other measures) was a ‘positive-sum game’ (p. 265)
that was politically useful both for Congress and for the executive branch, as well as good
for the country as a whole. These observations are consistent with a story in which Congress
1
In recent years, the official name has changed to ‘Trade Promotion Authority,’ but in this paper we will
use the more traditional term.
1
uses FTA to delegate significant authority over trade policy to the executive branch because
it does not trust itself, through the non-cooperative process of Congressional bargaining, to
achieve a desirable outcome, and in particular expects the executive branch to achieve more
trade-friendly, liberal outcomes than Congress would itself. This is the essence of the story
we offer in this paper.
Background. The earliest Congressional delegation of trade-policy authority was the 1934
Reciprocal Trade Agreements Act, which provided for temporary authority for the President
to negotiate a trade agreement that, provided it satisfied strict criteria, would be approved
in advance. This authority was used several times until modern fast-track authority was
first created in 1974 as part of the Trade Reform Act. This form of delegation retained more
discretion for Congress, because although it imposed a strict time limit for Congressional
decision making on any trade agreement and prohibited amendments to the agreement, it
did allow Congress to reject an agreement ex post. Ever since, FTA has been an integral part
of US trade policy, playing a key role in ratification of the Tokyo and Uruguay rounds, the
Canada-US Free Trade Agreement, and the North American Free Trade Agreement. (See
Koh (1992), Destler (1991), and Smith (2006) for concise histories.)
Some Earlier Approaches. There have been other notable attempts to interpret FTA.
Conconi et al. (forthcoming) suggest an interpretation of FTA as a way of enhancing US
bargaining power relative to the foreign government that is party to a trade negotiation. The
model relies on the insight that it is sometimes advantageous to delegate bargaining to an
agent whose preferences are different from one’s own, in particular an agent who is less eager
to arrive at an agreement, in order to extract more concessions from the other bargaining
partner. Essentially, without the FTA, Congress is in effect bargaining with the foreign
government. A member of Congress from a district that depends on an export industry will
be very eager for an agreement, and may wish to delegate bargaining to the President, who
is interested in maximizing welfare of the average district and is therefore less eager for an
agreement and therefore more likely to be able to receive major concessions from the foreign
government.
2
This strategic bargaining-power argument is complementary to ours. In order to make
the distinction clear, we will artificially shut down the bargaining-power channel by adopting
the fiction that the US is a small-open economy.
Another approach to explaining FTA is offered by Lohmann and O’Halloran (1994). In
their model, the Congressional process without FTA leads to ‘log-rolling,’ as each member
of Congress in turn proposes a tariff to protect the dominant industry in his own district,
and each member of Congress votes in favor of all other members’ proposed tariffs in order
to ensure that his own tariff will in turn be approved. As a result, the outcome is inefficient,
high protection. Depending on parameters, a majority in Congress may prefer to hand
responsibility for trade policy setting over to the executive branch, which will set tariffs to
maximize weighted utility across districts (the weights depend on partisanship).
This story is similar to ours in that it does not depend on an external bargaining effect, but
rather on inefficiencies in Congressional tariff-setting that members of Congress themselves
seek to avoid by delegation. However, we are interested in economic determinants of FTA,
such as of the geographic distribution and size distribution of industries. Lohmann and
O’Halloran shut down this topic by assuming economically symmetric districts, in order
to focus on the political variables (such as partisanship) that are their main interest. In
addition, their approach has a number of disadvantages relative to ours. In particular,
the Congressional voting game in Lohmann and O’Halloran (1994) does not have a unique
equilibrium (because a folk theorem applies, but also because no member’s vote is pivotal),
and in particular free trade appears to be just as much of a valid equilibrium as the ‘logrolling’ one. Given that for much of the parameter space free trade will be preferred by a
majority of members, and given that in practice members of Congress certainly are able to
communicate with each other before voting in order to coordinate on the Nash equilibrium
that they prefer, the focus on the ‘log-rolling’ equilibrium is not fully persuasive. By contrast,
in our bargaining model, an unfettered Congress has a unique equilibrium (within the broad
class of stationary subgame perfect equilibria), so there is no equilibrium-selection issue.2
2
Technically, the bargaining game can have multiple equilibria, but they all provide the same payoffs.
In addition, our focus is on when FTA will be chosen, which is uniquely determined for each point of the
3
Our Approach. In our model of a (unicameral) Congress, each Congressional district is
represented by a legislator who is concerned with his district’s welfare only, whereas the
President cares about the whole country’s welfare.3 Each industry is concentrated in one or
more districts, so welfare of any district is closely related to the industry operating in that
district.
Trade policy formation takes place as a two-stage process: First, Congress decides by majority vote whether or not to grant FTA to the President, and then trade policy is determined
either by the President (if FTA is granted in the first stage) or by Congress (if FTA is denied
in the first stage). When FTA is granted, Congress either approves or disapproves the chosen
policy by the President without amending it. If Congress approves the President’s policy,
it goes into effect, otherwise no policy change occurs and the status quo prevails. When
FTA is not granted, trade policy is determined by Congressional bargaining as in Baron and
Ferejohn (1989).4 A legislator is selected randomly to propose a trade bill.5 If the proposal
receives a majority, the bill goes to the President and the President either approves or vetoes
it. If the bill is approved, it is implemented and the legislature adjourns. If the bill is vetoed
and Congress does not override the veto, then a new legislator (possibly the same as in the
previous period) is selected to propose a new trade bill. On the other hand, if the proposal
does not receive a majority, there is no change in welfare level of any district (the status quo
prevails) and the process is repeated with a new legislator to propose a new trade bill. In
their voting, legislators compare the current proposal with the alternative of continuing to
the next period.
parameter space.
3
This makes sense since, in the United States, legislators come from plurality elections in small districts
whereas the President is elected in national elections.
4
The adaptation of the Baron and Ferejohn model to this context is not trivial. One reason is that
distortionary tariffs mean that the size of the pie is affected by the outcome, and not merely the distribution
of the pie. Another reason is that status quo tariffs have a significant role in the equilibrium in some cases, as
we will see in Case 3 with different initial tariffs for different industries. There is no analogous complication
in the original Baron and Ferejohn model.
5
While random recognition does not mimic any actual procedures of a legislature, it is a useful device
for capturing the inherent uncertainty that legislators face in building distributive coalitions. Random
recognition is a way of modelling the fact that legislators do not know exactly which coalitions will form in
the future if the current coalition fails to enact the legislation. See Celik, Karabay and McLaren (2011) for
an extensive discussion of this point with historical examples.
4
This approach allows us to study the effect of a country’s internal political conflict on its
trade policy determination, and formalize how the “domestic special interest group pressures”
can “[provoke] extensive, ad hoc amendment of a negotiated trade accord” (Koh (1992, p.
148)) which Congress might wish to avoid by delegating discretion to the executive branch.
This exercise reveals a number of sharp predictions. First, FTA is always granted when
the industries are sufficiently symmetric in their geographic distribution, output levels, and
status quo tariffs. Second, FTA is never granted if an industry is operating in the majority
of districts. Third, sufficient asymmetries in the geographic distribution or output levels
of industries ensure that FTA will fail.6 Forth, sufficient asymmetries in initial rates of
protection across industries can prevent the economy from reaching free trade even if FTA
is granted.
Interpretation. The idea that members of Congress may feel empowered by a measure
that removes their own future freedom of action may be illustrated by a simple parable.
Consider a group of travelers who loathe and distrust each other and who are shipwrecked
on a remote island, each carrying some necessary supplies rescued from the sinking ship. If
they discover a loaded pistol left behind by some earlier explorer, they all suffer; knowing
that whoever wakes up first will be able to gain control of the firearm and obtain all of the
supplies for himself, no-one will be able to enjoy a proper night’s sleep. As a result, the
castaways decide, by majority vote, to destroy the weapon by dropping it in the volcano
before sundown. (Yes, the island has a volcano.)
As a helpful guide, in this analogy, the castaways are members of Congress; the gun is
the ability to amend a trade agreement; and the volcano is Fast Track Authority.
However, this story depends on the castaways’ situation being symmetric, with similar
abilities and endowments. The story may end differently if a bare majority of the castaways
happen to be unemployed ninjas, who are skilled at disarming an assailant. These would
expect to be able to win any conflict involving the firearm, and so they would not wish to
drop it into the volcano. This corresponds to a case in which a single industry dominates
6
The importance of geographical distribution in trade policy formation is also emphasized in McLaren
and Karabay (2004).
5
a majority of Congressional districts, which will be studied as Case 1 below, so that that
industry will be able to out-compete other industries in the Congressional bargaining game.
Somewhat more subtly, it also corresponds to a case in which a majority of districts are
dominated by industries with lower output and higher import-penetration rates than the
other industries, studied below as Case 2, because as will be seen, such industries also are
better at playing the Congressional tariff-bargaining game and so have an advantage. Enough
asymmetry of the sort described by Cases 1 and 2 will result in a failure of FTA to pass.
The idea of Congress preventing its own ruinous competition through non-cooperative
bargaining over policy has an important antecedent in the theory of self-imposed Congressional budget caps, as explored by Primo (2006). The core of the argument comes from
the dynamic theory of Congressional bargaining pioneered by Baron and Ferejohn (1989)
and Baron (1993), and applied to trade policy in Celik, Karabay, and McLaren (2011). A
core idea is that the agenda-setting power in Congress can shift over time in unpredictable
ways with elections, scandals and other events, and whoever sets the agenda will be able to
form a majority coalition that votes itself trade protection at the expense of industries not
in the coalition. If joint welfare is maximized by free trade and all districts are symmetric
and equally likely to possess the agenda-setting power of the proposer, then welfare of each
district is maximized by a commitment to free trade, and hence FTA. Violations of these
symmetry conditions then make it less likely that FTA will be approved.
The following section lays out our model. Section 3 derives the conditions under which
FTA will be approved, for the fully symmetric case and then for asymmetric Cases 1 through
3. The last section discusses the results and concludes.
2
Model
We consider a small open economy populated with a unit measure of individuals living in
N districts (where N > 3 and divisible by 3). There are M = 4 industries: one that
supplies a homogeneous numeraire good (good 0) produced with labor alone, and three
others, each of which supplies a homogeneous manufacturing good (goods 1 through 3)
6
produced with sector-specific capital alone. In particular, we assume that the production
technology for good 0 yields 1 unit of output per unit of labor input, and the technology
for each manufacturing good takes the following form: f (Ki ) = θKi , where Ki and θ denote
the amount of the sector-specific capital used in sector i and the economy-wide productivity
parameter, respectively. (Unless specified otherwise, we use index letters (i, j, k) only for
the manufacturing goods.)
Each district hosts one manufacturing industry along with the numeraire good industry.7, 8 In addition, each district is composed of a homogeneous population; each individual
residing in a given district is endowed with one unit of labor and also one unit of the same
type of sector-specific capital. Let the number of districts producing good i be denoted by
ni such that n1 + n2 + n3 = N . Districts that produce the same manufacturing good are
populated by the same number of individuals. To save on notation, we let Ki denote both
the total amount of type-i capital in a type-i district and the total number of individuals
3
P
residing in a type-i district. Given that the population is of unit mass,
ni Ki = 1.9 Let
i=1
qi denote the amount of good i produced in a district that hosts industry i, and Qi denote
the total amount of good i produced in the economy. Therefore, we have qi = θKi and
3
3
P
P
Qi = ni qi .10 This implies that
Qi = θ
ni Ki = θ. In addition, let p∗i and pi represent,
i=1
i=1
respectively, the exogenous world price of good i and its domestic price. On the other hand,
the numeraire good, good 0, has a world and domestic price equal to 1 (see footnote 14).
Thus, the total rent that accrues to capital in district i is pi qi = θpi Ki , and the total labor
income earned in district i is Ki .
7
Our results carry over even if more than one industry is allowed in each district as long as each resident
still holds only one sector-specific capital and in every district there is one industry with majority representation. This is true since each legislator will follow the interests of the median voter, who belongs to a
particular industry under the conditions assumed here.
8
We do not model the location choice of a particular industry, rather we take it as given. However, we
acknowledge that this choice may depend on the political influence an industry can exert in each location.
9
We allow only those districts that produce different goods to differ in the number of citizens residing.
This is done to simplify the notation. Alternatively, it is possible to allow each district (even the ones
producing the same good) to be populated by different number of individuals. All of our results continue to
hold.
10
To make things simple and analytically tractable, aggregate output of each industry is perfectly inelastic
in our setup. This is merely to eliminate some complexity, but there is some evidence that supply elasticities
tend to be quite low in practice; see Marquez (1990) and Gagnon (2003).
7
Each individual has an identical, additively separable quasi-linear utility function given
by
u = c0 +
3
X
ui (ci ) ,
i=1
where c0 is the consumption of good 0 and ci represents the consumption of good i = 1, 2, 3.
We assume that ui (ci ) = Ri ci − (c2i /2), where Ri > 0 and assumed to be sufficiently large.11
With these preferences, the domestic demand for good i, implicitly defined by u0i (d(pi )) = pi ,
is given by d(pi ) = Ri − pi . The linearity of demand is not crucial for the main results of our
paper, but it simplifies the analysis and permits a closed-form solution. The indirect utility
of an individual with income y is y + s (p), where p = (p1 , p2 , p3 ) is the vector of domestic
P
prices,12 and s (p) = 3i=1 [ui (d(pi )) − pi d(pi )] is the resulting consumer surplus.
Each district is represented by a single legislator who is concerned only with the welfare
of his own district. A district’s welfare is the aggregate utility of all individuals in that
district, which is equal to the total income plus the district’s share in total consumer surplus
and total tariff revenue (or subsidy cost) for each good. Hence, a district that produces good
i has a welfare (for i 6= j 6= k)
Wi (p) = Ki + pi θKi + Ki
X (Rl − pl )2
X
+ Ki
[(pl − p∗l ) (Rl − pl − Ql )] ,
2
l=i,j,k
l=i,j,k
(1)
where the first term is the district’s labor income (equal to one unit of good 0 output per
person), the second term is the capital rent, the third term is the consumer surplus captured
by that district, and the last term is the share of tariff revenue (or subsidy cost).13 Similarly,
we denote wi (p) as the welfare of an individual with a stake in industry i, hence
X (Rl − pl )2
X
wi (p) = 1 + pi θ +
+
[(pl − p∗l ) (Rl − pl − Ql )] .
2
l=i,j,k
l=i,j,k
(2)
To be more precise, we require Ri > p∗i + θ − Qi . This ensures that demand for good i is positive at all
prices that may occur in equilibrium. We also require p∗i > Qi for each price to be positive. See Lemmas 1
and 2 for the determination of optimal tariffs (hence optimal prices).
2
2
(R −p∗
12
i ) +(θ−Qi )
We restrict each domestic price to satisfy: 0 ≤ pi < pi , where pi = p∗i + i 2(θ−Q
. These limits
i)
ensure that we get an interior solution in prices.
13
We assume that tariff revenue (or subsidy cost) is distributed equally as a lump-sum transfer to each
individual.
11
8
Moreover, there is also the President, and unlike the legislators, she has a national constituency and cares about the welfare of the whole country. As a result, her welfare is
expressed as
W (p) =
3
X
ni Ki wi (p).
(3)
i=1
We consider an infinite-horizon model. Every period, there is a set of prices at which individuals make their production and consumption decisions, and enjoy the resulting welfare.
We restrict the set of policy instruments available to politicians and allow only for trade
taxes and subsidies. A domestic price in excess of the world price implies an import tariff
for an import good and an export subsidy for an export good. Domestic prices below world
prices correspond to import subsidies and export taxes.14 The status quo domestic prices at
the beginning of the game are denoted by ps = (ps1 , ps2 , ps3 ).
The timing of the trade policy formation game is given in Figure 1.15 First, Congress
decides whether to grant FTA to the President. FTA will be granted if the majority of
legislators vote for it. If it is granted, then the President proposes a tariff bill and legislators
vote yes or no without amending it.16 If accepted by Congress, the bill is implemented
and legislative process ends. Each district’s welfare thereafter is evaluated at these new
prices. If Congress rejects the President’s proposal, then all districts receive their status quo
payoffs forever. If FTA is not granted, on the other hand, Congress enters what we will
call the bargaining subgame where trade policy is determined by Congressional bargaining
as in Baron and Ferejohn (1989). A legislator is selected randomly (with equal probability
Without loss of generality, we assume that the tariff/subsidy on good 0 is equal to 0. Any tariff vector τ 0
yielding domestic prices p0 = p∗ + τ 0 with τ00 6= 0 can be replaced by τ 00 ≡ p10 [τ 0 − τ00 p∗ ] yielding p00 = p∗ + τ 00
0
without changing relative prices or any real values. Given that good 0 is the numeraire, this implies that
p000 = p∗0 = 1.
15
To simplify, we assume that a period in the trade policy formation game coincides with a production/consumption period.
16
Of course, in reality FTA is granted to allow the President to negotiate a trade agreement with foreign governments. As mentioned in the introduction, in order to close down the issues of strategic intergovernmental bargaining that are the focus of Conconi et al. (forthcoming), and to allow us to focus on the
intra-congressional competition that is our interest, we employ the fiction that FTA is granted in order to
give the President authority simply to choose a tariff policy. In practice, the calculus of whether or not to
authorize FTA would take both sets of issues into account.
14
9
for each legislator) to propose a tariff bill.17 If the proposal does not receive a majority,
the process is repeated with another randomly selected legislator (possibly the same as in
the previous period) to make a new proposal. If the proposal receives a simple majority,
it is brought before the President for approval. If the President accepts the proposal, then
it is implemented and each district’s welfare thereafter is evaluated at these new prices. If
the President vetoes it, then the same legislator may bring the same proposal to a vote in
Congress. If 2/3 of the legislators support the proposal (hence overriding the veto), then it is
implemented and the legislature adjourns. Otherwise, another randomly selected legislator
is selected to make a new proposal. Bargaining continues until a program is implemented.
Districts continue to receive their status quo welfare in every period until an agreement is
reached. (A fuller analysis of the bargaining game without the President can be found in
Celik, Karabay and McLaren (2011).)
[Insert Figure 1 here]
There are a couple of observations to make. First, it is straightforward to show that
P3
the aggregate welfare, W (p) =
i=1 ni Ki wi (p), is maximized at the free trade prices of
the three goods. Hence, the President would always propose free trade if she thinks that
Congress will agree to it.
Second, from equation (1), a manufacturing good affects (through its price) a district’s
welfare via three channels. The first channel, the rent that accrues to the specific factor, is
present if that good is produced in that district. The second channel is the consumer surplus
attained from the consumption of that good. The last channel is the tariff revenue (or subsidy
cost) due to trade. The effect of price through the first channel is always positive whereas
it is always negative through the second channel. Its effect through the third channel, on
the other hand, can be positive or negative (in fact the third channel is strictly concave in
all three prices with a unique maximum). This is true since good i’s price has two distinct
effects on tariff revenue/subsidy cost: (1) the direct effect (changing price while keeping
17
Therefore, the probability that the proposer represents industry i is equal to
10
ni
N.
imports/exports constant), and (2) the indirect effect through demand. These two effects
work in opposite directions. To see this, assume that good i is an imported good. First,
start from a price just above the world price. As we increase the price, the direct effect
leads to an increase in the tariff revenue whereas the indirect effect leads to a decrease (since
import demand goes down). Initially, the direct effect dominates, and therefore, raising the
price raises tariff revenue. When the price reaches a certain value, the indirect effect starts
dominating and the tariff revenue decreases if we further increase the price.
For the remainder of the analysis, let τ = (τ1 , τ2 , τ3 ) denote the tariff vector, where
τi = pi − p∗i . Therefore, we can rewrite equation (2) as
wi (τ ) = 1 +
(p∗i
X (Rl − p∗ − τl )2
X
l
+ τi )θ +
τl (Rl − p∗l − τl − Ql ) .
+
2
l=i,j,k
l=i,j,k
(4)
Notice that, given our parameter restrictions (see footnotes 11 and 12), the per-capita welfare
function given in equation (4) is strictly concave in all tariffs and has a unique maximum.
Similarly, let τ s = (τ1s , τ2s , τ3s ) describe the vector of status quo tariffs. It will prove helpful
to write down the change in the per-capita welfare over status quo when Congress agrees on
a tariff bill τ . To do so, simply evaluate equation (4) at τ = τ s and subtract it from wi (τ ),
which leads to
s
wi (τ ) − wi (τ ) =
(p∗i
+ τi −
+
X
p∗i
−
τis )θ
X (Rl − p∗ − τl )2 − (Rl − p∗ − τ s )2
l
l
l
+
2
l=i,j,k
[τl (Rl − p∗l − τl − Ql ) − τls (Rl − p∗l − τls − Ql )] .
l=i,j,k
After rearranging, this becomes
wi (τ ) − wi (τ s ) = θ(τi − τis ) −
1 X (τl + Ql )2 − (τls + Ql )2 .
2 l=i,j,k
(5)
The first term on the right-hand side of equation (5) is the per-capita change in capital rent
while the second term indicates the per-capita change in consumer surplus plus tariff revenue.
This representation is helpful as it allows us to express the per-capita welfare change in each
district as a function of each industry’s tariff and total output.
11
We can alternatively express the per-capita welfare as an increment over free trade. To do
so, repeat the same steps as above (or, alternatively, evaluate equation (5) at τ s = (0, 0, 0))
to obtain
"
#
1 X
2
wi (τ ) = wi (0) + θτi −
(τl + Ql ) − Q2l .
2 l=i,j,k
(6)
The first-best for each legislator is to maximize his district’s welfare without any constraints. Note that since each individual in a given district is identical, maximizing aggregate
district welfare Wi (τ ) is equivalent to maximizing per-capita welfare wi (τ ). For a legislator
representing industry i, let τ Ui = (τiUi , τjUi , τkUi ), i 6= j 6= k, denote the vector of trade taxes
that the unconstrained maximization problem leads to, i.e., τ Ui = arg max wi (τ ). Maximizτ
ing equation (6) with respect to τ leads to the following lemma.
Lemma 1. Unconstrained maximization of wi (τ ), i = 1, 2, 3, yields (for i 6= j 6= k)
τiUi = θ − Qi ,
τjUi = −Qj ,
τkUi = −Qk .
Thus, a recognized (selected) legislator would ideally demand an import tariff (or an
export subsidy) for the good his district produces (thereby protecting the industry he represents) whereas an import subsidy (or an export tax) for the other goods.18 Moreover, a
producer in a sector that produces a higher aggregate output Qi will prefer a lower tariff
(or export subsidy) for his own product than a producer in a sector that produces lower
aggregate output. The reason is as follows. Focus for now on the case of an imported good.
Recall the three channels we discussed before through which the tariff affects the per-capita
welfare of producers in industry i. Aggregate output, Qi , in this case does not affect the
first two channels (the rent and consumer surplus channels – of course, a higher Qi implies
higher total rent, but not higher rent per capital owner in industry i). What it does affect
is the third channel, tariff revenue. A higher value for Qi implies a weaker tariff revenue
18
Since
3
P
Qi = θ, θ − Qi > 0, ∀i.
i=1
12
effect since, at a given price and the other parameters, a higher value of Qi implies fewer
imports, hence a lower marginal tariff revenue for a given increase in tariff.19 Therefore, a
higher value of Qi implies a lower marginal benefit of the tariff, and a lower optimal tariff,
from the point of view of a sector-i producer. Parallel reasoning holds for an exported good.
It is natural to assume that the status quo prices are in the range defined by the unconstrained maximization problem. For example, a legislator representing a district that
produces good i has no reason to set τi above θ − Qi . Similarly, he has no reason to set τj6=i
below −Qj . Hence, we make the following assumption.
Assumption 1. The status quo prices satisfy the following: −Qi ≤ τis = psi − p∗i ≤ θ − Qi ,
for i = 1, 2, 3.
A value of τis = θ − Qi corresponds to the case in which the status quo tariff of good i
is at its optimum for the districts that produce good i, while τis = −Qi corresponds to the
case in which it is at its optimum for the districts that produce good j 6= i. Accordingly,
the status quo corresponds to the optimal tariff vector for the districts that produce good i
when (τis , τjs , τks ) = (θ − Qi , −Qj , −Qk ).
Below, we will first describe the model in greater detail. After that, as a benchmark, we
will analyze a fully symmetric case in which each industry has the same output, same status
quo tariff and the same representation in Congress. We will then relax each of them one at
a time.
3
Characterization of equilibrium
Let us look at the problem more in detail. First, if ni ≥ 2/3 for any i, the problem becomes
trivial; legislators representing industry i will have enough seats to overturn a possible veto
19
The same conclusion holds for a comparison between two industries i and j even if, although Qi > Qj ,
the demand parameter Ri is sufficiently higher than Rj that at a common tariff, imports of good i exceed
those of good j. The reason is that an increase in Ri , holding all prices and other parameters constant,
raises industry i imports, increasing the marginal tariff revenue from the tariff on good i, but at the same
time raises domestic consumption of good i, raising the marginal consumer surplus loss from the tariff on
good i. The two effects cancel each other out, with the result that the demand parameters Ri have no effect
on tariff preferences.
13
by the President. Hence, the legislators that represent industry i refuse FTA and, with the
discount factor approaching 1, will subsequently be able to achieve their first-best payoff
in the legislative bargaining subgame. For the remainder of the analysis, we assume that
ni < 2/3, ∀i. Second, as a tie-breaking rule, in case of indifference between payoffs under
FTA and under no FTA, we will assume that FTA is preferred.
If Congress grants FTA in the first stage, the President chooses τ so as to maximize total
welfare while making sure that Congress does not reject it. If Congress does not grant FTA,
then Congress plays a bargaining game to determine the tariff vector, with a randomlyselected member serving as a proposer each period until an agreement is reached. Each
legislator is interested in maximizing his own district’s welfare, but even a legislator who has
been selected as the proposer may not be able to achieve the first-best payoff for his district.
The reason is that in order to build a veto-proof coalition, he may need to compromise a
certain fraction of his payoff and choose a favorable price for at least one of the other two
industries. We refer to this situation as the proposer selecting a ‘coalition partner’ (or simply
‘forming a coalition’).
As common in multi-person bargaining problems, there may be many subgame perfect
equilibria (SPE) in this game.20 We focus on stationary subgame perfect equilibrium (SSPE)
whereby the continuation payoffs for each structurally equivalent subgame are the same.21 In
a stationary equilibrium, a legislator who is recognized to make a proposal in any two different
sessions behaves the same way in both sessions (in the case of a mixed-strategy equilibrium,
this means choosing the same probability distribution over offers in both sessions). Hence,
stationary equilibria are history-independent. To make our results as clear as possible, we
focus on the case in which the discount factor (denoted by δ) approaches 1 in the limit.22
20
Baron and Ferejohn (1989) show that any outcome (in their game that means any division of the dollar)
can be supported as an SPE using infinitely nested punishment strategies as long as there are at least five
players and the discount factor is sufficiently high. Li (2009) shows that even with three players, there is a
vast multiplicity of SPE.
21
Baron and Kalai (1993) argue that stationarity is an attractive restriction since it is the “simplest”
equilibrium and so it requires the fewest computations by agents.
22
This may be interpreted such that the time length between any two offers (periods) is infinitesimally
short.
14
When a legislator is recognized to make a proposal in the bargaining subgame, he has
an incentive to propose a tariff bill that will be accepted, since if rejected, he faces the risk
that his district might be worse off by the bill adopted in the future. In equilibrium, in
accordance with the “Riker’s (1962) size principle,” any proposal will be accepted with the
minimal number of industries to form a veto-proof coalition. This is true since increasing
the number of industries in the coalition would increase the costs without increasing the
benefits.
Let the per -period equilibrium welfare of a district producing good i, evaluated at the
beginning of a period, before a proposer has been selected, be denoted as Vi . This is also the
per -period equilibrium welfare a district expects in the following period in the event that the
period ends without a bill passed, and so we will also call it the ‘continuation payoff.’ (Recall
that we are focussed on the limiting case as δ → 1.) We can also express the continuation
payoff of a district producing good i on a per capita basis: vi =
3.1
Vi
.
Ki
Fully Symmetric Benchmark
In this benchmark, we assume
n1
N
=
n2
N
=
n3
N
= 13 , Q1 = Q2 = Q3 =
θ
3
and τ1s = τ2s = τ3s .
The following observations are in order. First, any two-industry coalition can overturn the
President’s veto, so the President’s veto power is ineffective. Second, under FTA, it is
easy to see that the President will choose free trade. Recall that the aggregate welfare is
maximized at free trade prices. Therefore, when industries have symmetric status quo tariffs
(as assumed here), their status quo welfare is bounded above by what they enjoy in free
trade. This, in turn, implies that there will be no objection by the members of Congress
when the President chooses free trade under FTA. Third, as we show below, the legislative
bargaining makes each industry worse off compared to free trade, and therefore each industry
will choose to delegate the decision-making authority to the President in the first stage. All
these observations imply that under this benchmark, FTA is granted to the President in the
first stage and she chooses free trade in equilibrium.
In order to analyze FTA decision, we need to use backward induction. We first find the
15
ex ante expected welfare of each industry in the legislative bargaining subgame (when FTA
is not granted), then compare it with the one under FTA and show that the latter is greater
than the former for all industries so that FTA is granted in the first stage.
To do so, assume that Congress has not granted FTA and a legislator representing a
district which produces good i is recognized to propose a tariff vector, τ i . To obtain the
majority support in Congress, the proposal must make one of remaining two industries happy.
Suppose industry j 6= i is chosen as a partner. We assume that a legislator votes yes to a
proposal if and only if the benefits accruing to his district from the current proposal is at
least as high as the expected payoff it obtains in case the proposal does not pass.23 Thus,
legislators who represent districts that produce good j 6= i would say yes if and only if24
wj (τ i )
δvj
≥ wj (τ s ) +
.
1−δ
1−δ
The left-hand side of the above inequality indicates the discounted per-capita welfare a
district that produces good j obtains at the proposed tariffs, whereas the right-hand side is
the discounted expected per-capita payoff if bargaining is carried over to the following period
(the status quo welfare for the current period and the continuation welfare thereafter).
The values of vj are endogenous, as they are determined by the equilibrium tariff bill
and the equilibrium probability of being in a winning coalition. However, any recognized
legislator will take them as given when designing the tariff bill. Moreover, the recognized
legislator will choose τ such that the constraint is satisfied with equality, which means
that wj (τ ) = (1 − δ)wj (τ s ) + δvj in equilibrium. In the limit as δ goes to 1, this reduces
to wj (τ ) = vj .25 Hence, the recognized industry-i representative’s maximization problem
becomes
max wi (τ ) s.t. wj (τ ) = vj .
τ
23
(7)
In other words, we rule out weakly dominated strategies. In the absence of this assumption, a legislator
may choose to say yes to an otherwise unacceptable proposal if he believes that the proposal will receive a
majority support even without his vote. This implies there would be an equilibrium in which all legislators
vote yes to every proposal.
24
Note that districts that accommodate the same industry are identical, so if this inequality holds for one,
then it also holds for all.
25
To be more precise, when wj (τ s ) < vj (wj (τ s ) > vj ), the proposer offers the coalition partner an ex post
payoff that is infinitesimally below (above) vj . In either case, lim wj (τ ) = vj .
δ→1
16
As defined before, vj is the welfare an individual with a stake in industry j expects at
the beginning of a period; hence, it is a weighted average of possible ex post payoffs the individual may obtain depending on the identity of the proposer. Since the ex post per-capita
welfare function given in equation (4) is independent of status quo tariffs, so are the resulting equilibrium tariffs and payoffs found as a solution to expression (7). Intuitively, when
legislators are very patient, they place no weight on one-period gains (or losses) regardless
of how large they can be.
As in Baron and Ferejohn (1989), in an SSPE with δ close to 1, generically the proposer
randomizes between the two other industries in choosing a coalition partner. (In fact, in the
fully symmetric case, randomization occurs for any value of δ.) The proof is in the appendix,
but the crux of the idea can be summarized as follows. In an SSPE, by definition, if proposer
i ever chooses industry j with probability 1, then (due to stationarity) he always will choose
industry j with probability 1. But this means that industry j has enormous bargaining
power, and consequently at any given date, it will be less attractive for i to choose j than
the other industry – a contradiction. Let s denote the probability that i will choose j, and
hold constant the behavior of the other players when they are proposers. A reduction in
s lowers j’s continuation payoff, hence bargaining power, and raises k’s bargaining power
(i 6= k 6= j). Therefore, a critical value of s exists at which i is indifferent between the
two potential coalition partners, and this is the equilibrium value. The proper proof must
take into account boundary conditions as well as the fact that each player’s probability
over partners is endogenous, and it turns out that when all three players’ probabilities are
determined together, the equilibrium choice of probabilities is not unique, although the
payoffs are.26 We present the outcome of the legislative bargaining subgame in the following
lemma.
Lemma 2. The fully symmetric legislative bargaining subgame has an SSPE in which a
26
For a formal proof of payoff uniqueness, see our companion paper Celik, Karabay and McLaren (2011).
The same multiplicity is also present in the standard symmetric Baron-Ferejohn game, see Celik and Karabay
(2011). Eraslan (2002) shows that all SSPE in the Baron-Ferejohn game are payoff equivalent when the
recognition probabilities are asymmetric.
17
selected legislator representing a district which produces good i proposes a tariff τi =
θ
3
for
the good his district produces, a tariff τj = 0 for good j 6= i where j is selected randomly, and
a tariff τk = − 3θ for the remaining good. The first proposal receives a two-thirds majority
and Congress adjourns after the first session. All SSPE are payoff equivalent.
Proof. See appendix.
Thus, the logic of congressional bargaining imposes different levels of protection for different industries even if all industries are ex ante identical. In such a case, most other models
would predict τ1 = τ2 = τ3 , whereas in our model there would be three separate levels of
tariff.
We next present the main result of this section.
Proposition 1. When industries are ex ante identical, they all expect a lower per-capita
welfare in the legislative bargaining subgame than their corresponding free trade payoffs, i.e.,
vi < wi (0) for all i. Hence, all legislators vote for FTA in the first stage, the President
chooses free trade and Congress agrees to it.27
Proof. See appendix.
The competition for rent sharing is the harshest when bargaining power is symmetrically
distributed. Under the legislative bargaining subgame, the representatives in Congress will
vote for a bill that they do not like, because with the dynamic bargaining, they are afraid
that if the current bill does not pass, it will be replaced with something that they like even
less. Each industry knows that total welfare will be lower compared to free trade as tariffs
27
The same result obtains for any number of manufacturing industries. If there are M symmetric manufacturing industries, the support of M2−1 industries is required besides the industry the proposer belongs.
The respective ex post tariffs in this case are
τi
τj
τk
M −1
θ, for the proposer industry,
2M
M −1
= 0, for the
partner industries,
2
θ
M −1
= − , for the
remaining industries.
M
2
=
18
are introduced by the bargaining, but no-one knows who the ex post beneficiary will be.
Consequently, given the symmetry among industries, all coalition partners will be happy to
accept a payoff that is worse than free trade rather than being the excluded industry. As
δ → 1, this is also the payoff they ex ante expect from the bargaining. Knowing this, each
representative optimally delegates its decision-making authority to the President and enjoys
free trade welfare rather than playing this destructive bargaining subgame. Referring back
to our castaway analogy, since each castaway has the same chance to take possession of the
firearm, they all prefer to ditch the gun rather than worrying about who will get it first.
3.2
Asymmetric Configurations
In this subsection, we explore the implications of asymmetric configurations. We do so by
relaxing each industry characteristic one at a time. In Case 1, we allow for asymmetric
geographic distribution while keeping total outputs and status quo tariffs equal across industries. We then analyze the effects of asymmetric outputs in Case 2 while keeping the
other two variables equal across industries. Finally, in Case 3, we analyze asymmetric status
quo tariffs while holding other variables symmetric across industries. These asymmetries
introduce a rich set of predictions regarding the FTA decision.
Case 1 Asymmetric industry dispersion
Without loss of generality, throughout Case 1, we assume
n1
N
>
n2
N
>
n3
N
but still Q1 =
Q2 = Q3 and τ1s = τ2s = τ3s . When industries are symmetrically distributed (hence they have
identical political representation in Congress), presidential veto does not play a role since
any two-industry coalition can reach 2/3 majority which is enough to bypass the presidential
veto. This is no longer true under asymmetric industry dispersion. In this case, the legislative
bargaining subgame depends on how the President practices her veto power. For simplicity,
we will assume that when using her veto power in the bargaining subgame, the President
commits to free trade such that she will veto proposals that dictate a tariff vector (τ1 , τ2 , τ3 ) 6=
19
(0, 0, 0).28
Case 1a:
n1
N
>
1
2
>
n2
N
>
n3
N
As before, since τ1s = τ2s = τ3s and the aggregate welfare is maximized at free trade prices,
if FTA is granted in the first stage, the President chooses free trade and Congress approves
it. If FTA is not granted, we show that industry 1 does strictly better than free trade in the
bargaining subgame.
It is helpful to analyze this case in detail. Notice that industry 1 controls enough seats
to pass a proposal in Congress without the support of any other industry, where in such
a case it has to propose free trade due to the presence of presidential veto. However, as
we argue here, by forming a veto-proof majority with another industry, it will do strictly
better than its free trade payoff. Consider the following observations. First, industry 1 has
to be a member of any winning coalition, otherwise no proposal will pass in Congress since
n2 +n3
N
< 12 . In other words, when either industry 2 or industry 3 is chosen as a proposer, they
have to choose industry 1 as a coalition partner with probability 1. Second, in the event
that industry 1, as a proposer, offers a tariff vector that is different than free trade, it has
to get the support of one of the other two industries to override the presidential veto, since
n1
N
< 23 . There are two subcases to consider in forming such a veto-proof majority. In the
first subcase, when
1
3
>
n2
N
>
n3
,
N
industry 1 can randomize between industry 2 and industry
3 in choosing its coalition partner and thus has a very strong bargaining position. In fact,
in the limit as δ goes to 1, it is easy to show that industry 1 can obtain its first best, τ U1 ,
in equilibrium. In the second subcase, when
n2
N
>
1
3
>
n3
,
N
as a proposer, industry 1 has to
choose industry 2 as a coalition partner. This implies that industry 1 cannot obtain its first
best anymore, but even in that case, it can still do better than free trade. This is true since
unlike industry 2, it has to be a member of any winning coalition (Consider the case when
industry 3 is the proposer, for example.) These observations together entail that industry 1
28
We assume that the President commits to free trade only when using her veto power. When proposing a
trade policy under FTA, she does not commit to free trade but rather chooses a tariff vector that maximizes
her welfare under the constraints she faces. This implies that free trade does not necessarily result under
FTA. See Case 3 for an example.
20
can do better than free trade by forming a veto-proof coalition and hence will vote against
FTA in the first stage.
Lemma 3. In Case 1a, FTA does not pass, and industry 1 obtains a payoff in excess of its
free-trade payoff in the subsequent bargaining subgame.
Proof. See appendix.
Case 1b:
1
2
>
n1
N
>
n2
N
>
1
3
>
n3
;
N
Q1 = Q2 = Q3 ; τ1s = τ2s = τ3s
This case is similar to the second subcase of Case 1a except that for a proposal to pass
in Congress, industry 1 does not have to be in every winning coalition anymore. This is true
+n3
since now industry 2 can form a coalition with industry 3 ( n2N
> 12 ) and propose free trade
(they cannot propose anything else since the presidential veto is binding). On the other hand,
only industries 1 and 2 can form a veto-proof majority to override the President’s veto and
propose something other than free trade. These two observations imply that compared to
the second subcase of Case 1a, industry 1 has a weaker bargaining position whereas industry
2 has a stronger bargaining position. In addition, although both industries 1 and 2 have
the option of forming a coalition with industry 3 and enjoying free trade welfare (since any
two-industry coalition involving industry 3 cannot override the presidential veto), they will
not do so because each can do strictly better if they form a coalition together and bypass
the presidential veto. Here, industry 3 is too small to be a valuable partner. On the other
hand, when industry 3 gets the chance to make a proposal, it will have to get a unanimous
consent from Congress. This is true since any two-industry coalition with industry 3 being
the proposer has to offer free trade but neither industry 1 nor industry 2 will accept this
proposal given their strong bargaining positions.
In short, in the bargaining subgame, both industries 1 and 2 have strong positions and
both will enjoy payoffs that are above their corresponding free trade payoffs. Hence, they
will vote against FTA and FTA will not pass.
Lemma 4. In Case 1b, FTA does not pass, and both industries 1 and 2 obtain payoffs in
excess of their free-trade payoffs in the subsequent bargaining subgame.
21
Proof. See appendix.
Case 1c:
1
2
>
n1
N
>
1
3
≥
n2
N
≥
n3
;
N
Q1 = Q2 = Q3 ; τ1s = τ2s = τ3s
This case is similar to the first subcase of Case 1a except that industry 1 has no longer
majority in Congress and thus, does not have to be in every winning coalition. Industry 2
and industry 3 can form a coalition and propose free trade (since the presidential veto is
binding). On the other hand, industry 1 can, as before, randomize between industry 2 and
industry 3 in choosing its coalition partner and any coalition involving industry 1 makes the
President’s veto power ineffective, since
n1 +nj
N
> 32 , for j = 2, 3.
In this case, although industries 2 and 3 have the option of forming a coalition together
and proposing free trade, being uncertain about who will be in the winning coalition when
industry 1 is the proposer will lead to an expected payoff that is worse than free trade for
both. As a result, in the bargaining subgame, industry 1 still has a strong position (although
cannot achieve its first best) but industry 2 and industry 3 have a weak position such that
they do not obtain a payoff that is better than free trade. Hence, industry 2 and industry 3
will vote for FTA and given that
n2 +n3
N
> 12 , FTA will pass.
Lemma 5 In Case 1c, FTA always passes in the first stage, the President subsequently
proposes free trade and Congress agrees to it.
Proof. See appendix.
Lemmas 2 through 5 lead to the following proposition.
Proposition 2. When industries differ only in their geographic distribution, FTA will pass
if and only if
1
2
>
n1
N
>
1
3
≥
n2
N
≥
n3
.
N
To summarize this section, in the event of asymmetric political clout due to differences
in the nj ’s, if one industry is dominant (Case 1a, with n1 > 12 ), then FTA is not granted.
This is analogous to the case in the introduction in which a bare majority of castaways are
unemployed ninjas; they know that they will win any competition for resources, so they
22
welcome the competition. The outcome for Case 1b is similar, because industries 1 and 2
can form a veto-proof majority but neither industries 1 and 3 nor industries 2 and 3 can.
Thus a bare majority in Congress have power over a minority. On the other hand, in Case
1c, no industry has a majority, and no industry needs more than one other partner to form a
veto-proof majority,29 so the distribution of bargaining power is relatively symmetric, and all
industries dread the inter-industry congressional bargaining process, thus FTA is granted.
Case 2 Asymmetric industry output
Without loss of generality, throughout Case 2, we assume that Q1 > Q2 > Q3 . As stated
earlier, since τ1s = τ2s = τ3s and the aggregate welfare is maximized at free trade prices, if
FTA is granted in the first stage, the President chooses free trade and Congress approves it.
If FTA is not granted, larger industries that produce more output tend to benefit less from
congressional negotiations over tariffs than smaller industries.30 The reason is that such an
industry will generate fewer imports (since it will satisfy more of domestic demand from
domestic production), and so the tariff revenue produced by a given tariff will be small; but
this means that if a large industry is a member of the coalition that forms the tariff bill,
the coalition partner will receive little benefit from a tariff on the large industry, and so will
be unwilling to agree to a high tariff. As a result, the largest industry (industry 1) always
obtains a lower welfare under the legislative bargaining than under free trade if FTA is not
granted to the President. Hence, industry 1 always votes in favor of FTA. In addition, since
each industry has the same geographic dispersion and industry 2 produces more output than
industry 3, the final decision to grant FTA depends on whether industry 2 is better off under
FTA or not.
We show that if industry 2’s output is large enough, industry 2 does worse under the
legislative bargaining than under free trade (which will result if FTA is granted) and therefore
29
In Case 1c, unlike in Case 1b, even industry 3 can form a veto-proof coalition if it forms a partnership
with industry 1.
30
In particular, as we show in the appendix (see equation (12)), each industry’s payoff is decreasing in its
own output and increasing in other industries’ output.
23
industry 2 also votes in favor of FTA (in addition to industry 1) and FTA is granted. On
the other hand, if industry 2’s output is small enough, then we can show that industry 2
does better (along with industry 3) under the legislative bargaining and therefore FTA is
not granted. We can state these outcomes in detail with the following proposition, which is
illustrated by Figure 2.
Proposition 3. When industries produce asymmetric outputs, FTA will not be granted if
√ Q2 < 2θ 1 − 3√73 whereas FTA will be granted if Q2 > 3θ and the President will choose free
√ trade. On the other hand, when 2θ 1 − 3√73 ≤ Q2 < 3θ , there is a critical value of Q3 , say
Q3 (Q2 ), a decreasing function of Q2 , such that if Q3 < Q3 , FTA is not granted; whereas if
Q3 > Q3 , FTA is granted and free trade will be adopted by the President.
Proof. See appendix.
[Insert Figure 2 here]
Another way of looking at this is, again, through the castaway analogy of the introduction.
Figure 2 shows that the region in which FTA is rejected is the lower-left-hand corner of the
cone under the 45◦ line. Since, by assumption, Q1 > Q2 > Q3 and Q1 + Q2 + Q3 = θ, this
is the same as saying that FTA will be granted provided that the largest industry is not too
large relative to the smaller industries. Again, it is asymmetry in power that leads FTA to
be rejected. In this case, holding constant the number of seats represented by each industry
(and thus the size of the population dependent on each industry), a larger industry has
less ability to compete for tariffs, and thus less power in the bargaining subgame than a
smaller industry. If industry 1 is large enough relative to industries 2 and 3, the smaller two
industries understand that they can successfully gang up on it in the bargaining subgame,
just like the ninja castaways, and as a result have no interest in FTA.
Case 3 Asymmetric status quo tariffs
24
Without loss of generality, throughout Case 3, we assume that τ1s > τ2s > τ3s . There are
two points to make here. First, given that all industries are symmetrically dispersed and
their outputs are the same, each industry will have the same ex ante expected payoff in
the bargaining subgame (recall that we analyze the equilibrium when the discount factor is
approaching 1 in the limit, so one period gains or losses are unimportant). Since total welfare
is maximized under free trade, this implies that all industries will be worse off under the
bargaining subgame compared to free trade. Second, once FTA has been granted, Congress
has the option to reject the President’s proposal and return to the status quo. Therefore,
under FTA, the President cannot make two industries (which constitute the majority in
Congress) worse off compared to the status quo. As a result, there are two possibilities to
explore. In the first scenario, if at least two industries prefer free trade to the status quo, the
President will choose free trade under FTA and since the ex ante expected payoff of each
industry is lower under the bargaining subgame compared to free trade, FTA will be given
in the first stage. In the second scenario, if two of the three industries prefer the status quo
to free trade, then the President must offer a tariff vector that will not make the majority
of the industries worse off compared to the status quo. In such a case, the President cannot
choose free trade but will choose a tariff vector that is in the neighborhood of free trade. As
we show in the appendix, all industries will still do strictly better under FTA than what they
expect to get under the legislative bargaining. This is true since due to harsh competition
between industries, the legislative bargaining makes the total available surplus shrink too
much whereas under FTA, the President still chooses a tariff vector that is around free trade
and thus the total surplus available is not as small as in the case of bargaining subgame.
These observations imply that under Case 3, all industries will vote for FTA, and FTA will
always be granted to the President.
Let’s focus on the second scenario described above where two of the three industries prefer
the status quo to free trade. Since each industry’s payoff is increasing in its own protection
and decreasing in other industries’ protection (see equation (14) in the appendix), these two
industries that prefer the status quo to free trade must be industries 1 and 2 (remember
25
τ1s > τ2s > τ3s ). This automatically implies that industry 3’s status quo payoff is lower
compared to free trade (all three industries cannot be better off under the status quo since
free trade maximizes the aggregate welfare). When FTA is granted, the President will offer
a tariff vector that is as close as possible to free trade while keeping median industry’s
(industry 2) payoff constant at its status quo value. This makes industry 1 worse off and
industry 3 better off compared to the status quo. Notice that even in this case, in addition
to industries 2 and 3, industry 1 also prefers FTA, since it would do even worse under the
legislative bargaining if FTA had not been granted. These results are outlined in detail in
Proposition 4.
Proposition 4. When industries differ only in their status quo tariffs, FTA is always
granted. However, unlike before, the President cannot always choose free trade when FTA
√
√
(1+ 3)θ
(1− 3)θ
s
is granted. In particular, when τ2s >
or
τ
<
, free trade will be chosen by
2
6√
6√
(1− 3)θ
(1+ 3)θ
the President. On the other hand, if
≤ τ2s ≤
, there is a critical value of
6
6
τ3s , say τ s3 (τ1s , τ2s ), which is decreasing in τ1s and increasing in τ2s , such that if τ3s < τ s3 , the
President will offer a tariff vector τ P 6= (0, 0, 0) that makes the median industry (industry
2) indifferent to the status quo, whereas if τ3s > τ s3 , the President chooses free trade.
Proof. See appendix.
We can summarize Case 3 as follows. Because in this case each industry controls the same
number of seats and produces the same level of output, power is symmetrically allocated in
the bargaining subgame. Each castaway has the same probability of acquiring the gun. As a
result, every member of Congress prefers FTA to the bargaining subgame, and so FTA will
always be granted.
One wrinkle appears that is not present in Cases 1 and 2, namely that under FTA the
President may not offer free trade. If there is enough asymmetry in initial tariffs, it is quite
possible that a majority of industries with high tariffs will prefer the status quo to free trade,
and so the President will be forced to make the best of FTA by offering the closest thing to
it that makes the median industry as well off under the status quo. This involves letting that
26
median industry keep a positive tariff, while saddling the other industries with a negative
tariff. If the median industry only slightly prefers the status quo to free trade, then the
tariff vector offered will be only a slight perturbation away from free trade. This outcome
is summarized on Figure 3, which shows, for a given value of τ1s , the values of τ2s and τ3s for
which the President will propose a tariff vector different from free trade – the region marked
τ P 6= 0 in the figure. The right-hand boundary of this figure is τ1s (which we have set at the
value τ1s = 0.3θ for illustrative purposes), due to our convention that τ1s > τ2s > τ3s . The
upward-sloping curve plots the values of τ s3 (τ1s , τ2s ) = τ s3 (0.3θ, τ2s ), the critical value of τ3s
below which industry 2 prefers the status quo to free trade. If we allow τ1s to increase, this
curve will shift down (since τ s3 (τ1s , τ2s ) is decreasing in τ1s ) at the same time as the τ1s = 0.3θ
boundary shifts to the right. The point is that for a given value of τ1s , industry 2 is more
likely to acquiesce to free trade, the lower is its initial tariff and the higher is industry 3’s
initial tariff. In addition, if the initial point is, say, point A, so that industry 2 would
refuse free trade, then if we increase τ1s sufficiently, the τ s3 (τ1s , τ2s ) curve will shift down until
eventually A is above the curve. At that point, industry 2 will prefer free trade to the status
quo, and so the President will offer free trade and it will be accepted.
[Insert Figure 3 here]
4
Conclusion
In this paper, we analyze an important institution of trade policy: Fast-track authority
(FTA), by which Congress delegates a portion of its trade-policy authority to the executive
branch, and which has been a feature of almost every major trade agreement entered into
by the United States. We suggest an interpretation in which FTA is used by Congress to
forestall destructive competition between its members for protectionist rents, competition
that can leave a majority or even all members of Congress worse off ex ante. In our model,
each district hosts an industry and therefore each district’s welfare is closely related to the
industry operating in it. We model the congressional bargaining game as in Baron and
27
Ferejohn (1989), and analyze the conditions under which a majority of members of Congress
will choose to vote for FTA.
Our analysis shows the following. First, FTA is never granted if an industry is operating
in the majority of districts. This is true since if an industry operates in a majority of
districts, it can benefit at the expense of other districts under no FTA. Second, the more
equally distributed are the industries across districts and the more similar are the industries’
sizes, the more likely it is that FTA is granted. This is true since competition between rents
is most punishing when bargaining power is symmetrically distributed, and in that case the
ex ante expected welfare of each district is lower when Congress does not grant FTA to the
President. Third, if existing levels of protection are very different across industries, even if
FTA is granted, it may not lead to free trade because a majority of industries may prefer
the status quo to free trade.
Notice that even though we use small open economy model in which prices are taken as
given, the logic should apply to the more realistic case of a large country negotiating a trade
agreement, in which case the issues of strategic bargaining that are the focus of Conconi et
al. (forthcoming) would also arise.
Appendix
Proof of Lemma 2. Here, we present a general proof for any industry configuration. When
a legislator representing industry i is selected as the proposer and chooses industry j 6= i as
the coalition partner, we denote the chosen tariffs as τ = (τiij , τjij , τkij ), where τiij is the tariff
industry i gets, τjij is the tariff industry j gets and τkij is the tariff industry k 6= i, j gets.
Now, suppose a legislator representing industry i is selected as the proposer and he
chooses industry j 6= i as the coalition partner. His maximization problem is
max wi (τiij , τjij , τkij ) s.t. wj (τiij , τjij , τkij ) > (1 − δ)wj (τ s ) + δvj ,
τiij ,τjij ,τkij
The recognized legislator will choose τ such that the constraint is satisfied with equality.
Furthermore, in the limit as δ → 1, the constraint can be rewritten as wj (τ ) = vj . Hence,
28
the maximization problem becomes
max wi (τiij , τjij , τkij ) s.t. wj (τiij , τjij , τkij ) = vj .
τ
where
"
#
i
2
1 X h ij
2
s
= wi (τ ) +
−
−
τl + Ql − (τl + Ql )
,
2 l=i,j,k
"
#
h
i
X
1
2
wj (τiij , τjij , τkij ) = wj (τ s ) + θ(τjij − τjs ) −
τlij + Ql − (τls + Ql )2 .
2 l=i,j,k
wi (τiij , τjij , τkij )
s
θ(τiij
τis )
The Lagrangian can be expressed as
"
#
i
X h ij
1
2
2
ij
ij
ij
ij
(τi , τj , τk ) = θ(τi − τis ) −
τl + Ql − (τls + Ql )
2 l=i,j,k
#
"
h
i
X
1
2
τlij + Ql − (τls + Ql )2 − vj ,
+λij θ(τjij − τjs ) −
2 l=i,j,k
where λij is the Lagrange multiplier when a legislator representing industry i is selected as
the proposer and he chooses industry j 6= i as the coalition partner. It represents the cost
to the proposing legislator of obtaining the additional votes needed to pass the proposal.
The first-order conditions, after simplification, are
τiij =
θ
− Qi ,
1 + λij
τjij =
θλij
− Qj ,
1 + λij
τkij = −Qk .
We first show that, in an SSPE in which all proposers employ mixed strategies in choosing
their coalition partners, the value of λij is independent of the identity of the proposer and of
the coalition partner, i.e., λij = λ for all i 6= j, i, j = 1, 2, 3. This follows from the following
two observations. First, a legislator would employ a mixed strategy in choosing a coalition
partner only when the ex post payoff his district enjoys is the same under each alternative.
29
In other words, when a legislator representing industry i is selected as the proposer, he
randomly picks an industry as a coalition partner if, for all i 6= j 6= k,
wi (τiij , τjij , τkij ) = wi (τiik , τjik , τkik )
i
2
1 X h ij
2
s
−
⇔
−
τl + Ql − (τl + Ql )
2 l=i,j,k
i
2
1 X h ik
= θ(τiik − τis ) −
τl + Ql − (τls + Ql )2 .
2 l=i,j,k
θ(τiij
τis )
Using the equilibrium values of (τiij , τjij , τkij ) and (τiik , τjik , τkik ), we have



2
ij 2
2
ik 2
1
+
(λ
)
θ
1
+
λ
θ
2
2
θ
1
1
.
= θ
−
−
1 + λij
2
1 + λik 2
(1 + λij )2
(1 + λik )2
It is easy to see that this is possible only if λij = λik . Second, when industry j is chosen
as a coalition partner, the ex post welfare it is offered would be independent of the identity
of the proposer, because whoever is the proposer always offers an ex post welfare of vj to
this industry, otherwise the proposal is rejected. Thus, for any i 6= j 6= k,
wj (τiij , τjij , τkij ) = wj (τikj , τjkj , τkkj )
i
2
1 X h ij
2
s
−
⇔
−
τl + Ql − (τl + Ql )
2 l=i,j,k
2
1 X kj
2
kj
s
s
τl + Ql − (τl + Ql ) .
= θ(τj − τj ) −
2 l=i,j,k
θ(τjij
τjs )
Using the equilibrium values of (τiij , τjij , τkij ) and (τikj , τjkj , τkkj ), we have



2
ij 2
2
kj 2
θ
1  1 + (λ ) θ 
1 1+ λ
λij θ2
λkj θ2
.
−
−
=
1 + λij
2
1 + λkj
2
(1 + λij )2
(1 + λkj )2
Again, this is possible only if λij = λkj . Together with the earlier observation, λij = λkj =
λik , which implies that λij = λ for all i 6= j, i, j = 1, 2, 3. Next, we find the equilibrium value
of λ in an SSPE in which all proposers employ mixed strategies in choosing their coalition
30
partners. We first write down the equilibrium ex post per-capita welfare in three distinct
cases.
(i) when the districts that produce good j are selected as the proposer:
"
!#
2
2
2
X
θ
1
(1
+
λ
)
θ
wjproposer = wj (τ s ) +
−
− θ(τjs + Qj ) −
(τls + Ql )2
.
1+λ
2
(1 + λ)2
l=i,j,k
(ii) when the districts that produce good j are selected as a coalition partner:
"
!#
2
2
2
X
λθ
1
(1
+
λ
)
θ
wjpartner = wj (τ s ) +
− θ(τjs + Qj ) −
−
(τls + Ql )2
.
1+λ
2
(1 + λ)2
l=i,j,k
(iii) when the districts that produce good j are left outside the coalition:
!#
"
2
2
X
(1
+
λ
)
θ
1
2
−
(τls + Ql )
.
wjoutside = wj (τ s ) + −θ(τjs + Qj ) −
2
(1 + λ)2
l=i,j,k
We next express the equilibrium continuation welfare of a district on a per capita basis.
To do so, we need to introduce randomization probabilities. Let sij denote the probability
that a legislator representing a district that produces good i chooses the districts producing
good j as a coalition partner. Then, vj can be expressed as
vj =
ni
nj
[sji wjproposer + (1 − sji )wjproposer ] + [sij wjpartner + (1 − sij )wjoutside ]
N
N
nk
partner
outside
+ [skj wj
+ (1 − skj )wj
].
N
After simplification, this becomes
nk 1
θ 2 nj ni
vj = wj (τ )+
+ sij + skj
λ −θ(τjs +Qj )−
1+λ N
N
N
2
s
!
X
(1 + λ2 ) θ2
2
s
−
(τl + Ql ) .
(1 + λ)2
l=i,j,k
Next, observe that the maximization problem implies wjpartner = vj (since the constraint
is binding in equilibrium). Hence, it must be true that
3
X
wjpartner =
j=1
3
X
j=1
31
vj .
Also note that
3
n
n
X
nk n3 n1
n2 n2
n3 i
1
sij + skj
= s12 + s32
+ s13 + s23
+ s21 + s31
N
N
N
N
N
N
N
N
j=1
i6=k6=j
= (s12 + s13 )
n1
n2
n3
+ (s21 + s23 )
+ (s31 + s32 )
N
N
N
n1 + n2 + n3
N
= 1.
=
The condition
3
P
wjpartner =
j=1
3
P
vj can now be expressed as
j=1
3
X
3
3λθ2
−θ
τjs + Qj −
1+λ
2
j=1
X
(1 + λ2 ) θ2
−
(τls + Ql )2
2
(1 + λ)
l=i,j,k
3
X
3
θ2
=
(1 + λ) − θ
τjs + Qj −
1+λ
2
j=1
!
X
(1 + λ2 ) θ2
(τls + Ql )2
2 −
(1 + λ)
l=i,j,k
!
1
⇔λ= .
2
So, the value of λ can be determined without the knowledge of the randomization probabilities. Plugging the equilibrium value of λ into the tariffs we found earlier gives
τiij =
2θ
− Qi ,
3
τjij =
θ
− Qj ,
3
τkij = −Qk .
The continuation payoff of each industry can be determined easily by the condition
vj = wjpartner . Evaluating wjpartner at λ = 1/2 leads to
"
!#
2
2
X
θ
1
5θ
vj = wj (τ s ) +
− θ(τjs + Qj ) −
−
(τls + Ql )2
.
3
2
9
l=i,j,k
With Q1 = Q2 = Q3 = 3θ , the equilibrium tariffs are
θ
τiij = ,
3
32
(8)
τjij = 0,
θ
τkij = − .
3
The final step of the proof is to show that there is an interior solution to all of the
randomization probabilities (this is what we assumed at the beginning of the proof). Since
the continuation per -period, per-capita welfare is equal to ex post welfare when chosen as a
coalition partner (by the maximization problem), i.e., vj = wjpartner , we have
θ 2 nj ni
nk λθ2
+ sij + skj
λ =
.
1+λ N
N
N
1+λ
Evaluated at λ = 1/2, this becomes
sij
nj
nk
ni
+ skj
=1−2 .
N
N
N
For simplicity, let s12 = s1 , s23 = s2 and s31 = s3 . Then,
s1
n3
n2
n1
+ (1 − s3 )
= 1−2 ,
N
N
N
s2
n1
n3
n2
+ (1 − s1 )
= 1−2 ,
N
N
N
s3
n3
n2
n1
+ (1 − s2 )
= 1−2 .
N
N
N
It is easy to check that, when
n3
N
≤
n2
N
≤
n1
N
≤ 12 , there is an interior solution in which
si ∈ [0, 1] for all i. To see this, fix s3 and express s1 and s2 in terms of s3
s1 =
1 − 2 nN2 − (1 − s3 ) nN3
s2 = 1 −
n1
N
1 − 2 nN1 − s3 nN3
n2
N
,
.
h
n i
1−2 1
Any value of s3 ∈ 0, n3 N yields s1 , s2 ∈ [0, 1].
N
When
n1
N
=
n2
N
=
n3
N
= 13 , the above system reduces to s1 = s2 = s3 , so any s3 ∈ [0, 1] is
a solution.
33
Proof of Proposition 1. To express the equilibrium continuation payoff as a deviation
from an industry’s free trade payoff, evaluate equation (8) at τ s = (0, 0, 0) to obtain
"
!#
X
θ
1 5θ2
2
vj = wj (0) + θ( − Qj ) −
−
Ql
.
3
2
9
l=i,j,k
Evaluating equation (9) at Qi = Qj = Qk =
θ
3
(9)
leads to
vj = wj (0) −
θ2
.
9
(10)
Hence, for all j = 1, 2, 3, vj < wj (0) since θ > 0.
Proof of Lemma 3. Here, we prove that v1 > w1 (0), so FTA does not pass. Suppose on the
contrary that FTA passes. Given that
n1
N
> 12 , this is possible only when the representatives
of industry 1 say yes to FTA, which requires v1 ≤ w1 (0). Since industries 2 and 3 are too
small to form a coalition together, both will choose industry 1 as their partner when either
of them becomes the proposer. For a given value of δ < 1, let vi (δ) indicate the equilibrium
per-capita continuation payoff of industry i = 1, 2, 3. Both industries 2 and 3 will offer a
per -period payoff of (1 − δ)w1 (τ s ) + δv1 (δ) to industry 1. Given that industry 1 can always
propose free trade when it is the proposer, we have
v1 (δ) ≥
n1
(n2 + n3 )
w1 (0) +
[(1 − δ)w1 (τ s ) + δv1 (δ)] .
N
N
Solving for v1 gives
v1 (δ) ≥
n1
(n2 + n3 )
w1 (0) +
(1 − δ)w1 (τ s ).
N − δ (n2 + n3 )
N − δ (n2 + n3 )
Denote the right-hand side of the above inequality as v1min (δ). Note that lim v1min (δ) = w1 (0)
δ→1
s
(since w1 (τ ) ≤ w1 (0),
v1min
(δ) approaches w1 (0) from below as δ → 1).
Define w̃i (v), < 7→ <, by
w̃i (v) ≡ max wi (τ ) subject to wj (τ ) = (1 − δ) wj (τ s ) + δv,
τ
(11)
where i = 1, 2, 3, and i 6= j. In words, w̃i (v) is the (per -period) ex post payoff that industry
i is able to obtain for itself as the proposer when the equilibrium continuation payoff of the
34
coalition partner – industry j here – is v (assuming i and j can form a coalition that overturns
a possible veto by the President). This problem is symmetric for all players since ni ’s do
not matter once a proposer is selected. By equation (6), then, it follows that w̃i (v) − wi (0)
is the same for all i = 1, 2 or 3.31 Clearly, the derivative w̃i0 (v) < 0, so w̃i (v) is a strictly
decreasing function of v.32 Also note that w̃ has the property that lim w̃i (w̃j (v)) = v for any
δ→1
value of v. In other words, if, say, industry 2 has a continuation payoff of v2 = w̃2 (v), then
industry 1 can obtain at most v for itself when it is the proposer and chooses industry 2 as
the coalition partner.
Since we have assumed that all industries are very patient, we will focus on the limiting
case δ → 1 in the remainder of the proof. Unless otherwise stated, all payoffs are evaluated
in the limit as δ → 1 (so, we are not going to use ‘lim’ argument unless necessary).
There are two subcases to consider. First, suppose that
n2
N
≤ 13 . This is the scenario
in which industry 1 can form a veto-proof coalition with either of the other two industries.
Given that v1 ≤ w1 (0), industry 2’s as well as industry 3’s proposer payoff will be higher
than free trade. This follows from the observation that industry 2 (industry 3) can always
make itself better off than free trade by proposing a tariff vector that provides negative
protection to industry 3 (industry 2) while providing free trade welfare to industry 1, i.e.,
w̃j (w1 (0)) > wj (0), j = 2, 3. Given v1 ≤ w1 (0), this implies that w̃j6=1 (v1 ) > wj6=1 (0)
a fortiori. It also directly follows from the same observation that the industry that is left
outside the winning coalition will surely obtain a payoff that is less than its free trade payoff.
For i 6= j 6= k, denote wkij as the payoff industry k receives when industry i is the proposer
and it chooses industry j as the coalition partner. The value of wkij may certainly depend
on the identity of the proposer, but it is always true that wkij < wk (0). When industry 1 is
the proposer, it will either choose free trade or choose (possibly with a mixed strategy) one
of the other two industries to form a veto-proof coalition, so the highest industry j 6= 1 can
31
Note that we do not limit the domestic prices of the manufacturing goods to be identical. Hence, wi (0)’s
need not be equal.
32
If λ is the Kuhn-Tucker multiplier for the optimization in expression (11), then the envelope theorem
shows that w̃i0 (v) = −δλ < 0.
35
obtain is max {vj , wj (0)}. So,
vj ≤
nj
n1
nk
w̃j (v1 ) +
max {vj , wj (0)} + wjk1 , j 6= k 6= 1.
N
N
N
Since w̃j (v1 ) > wj (0) > wjk1 , it follows that vj < w̃j (v1 ), j = 2, 3. This means that
w̃1 (vj ) > w̃1 (w̃j (v1 )) = v1 , where we have used the two properties of w̃i described before:
w̃i0 (v) < 0 and w̃i (w̃j (v)) = v. Given that v1 ≥ v1min , w̃1 (vj ) > v1min = w1 (0), so industry 1,
as a proposer, would choose to form a coalition with one of the other two industries rather
than proposing free trade. This implies
v1 =
n1
(n2 + n3 )
max {w̃1 (v2 ), w̃1 (v3 )} +
v1 ,
N
N
which, after simplifying, reduces to v1 = max {w̃1 (v2 ), w̃1 (v3 )}. However, this constitutes a
contradiction since we had earlier found that w̃1 (vj ) > v1 for j = 2, 3. Hence, it must be
that v1 > w1 (0) when
n2
N
≤ 13 .
The other possible scenario is
n2
N
> 13 . In this case, a coalition between industries 1 and
3 is not veto-proof. So, industry 1 needs the support of industry 2 if it wants to obtain
a payoff that is strictly higher than free trade. First, assume that v2 ≤ w2 (0). In this
case, industry 1 would always form a coalition with industry 2 whenever it gets to make a
proposal, because w̃1 (v2 ) > w1 (0) as discussed earlier. Industry 2 would also always form a
coalition with industry 1 since we have v1 ≤ w1 (0) by assumption. Industry 3, on the other
hand, makes a proposal that will be accepted by all members of Congress, because given
that v1 ≤ w1 (0) and v2 ≤ w2 (0), industry 3 can obtain a payoff at least as much as its free
trade payoff. Hence,
v1 =
n1
(n2 + n3 )
w̃1 (v2 ) +
v1 .
N
N
This expression implies that v1 = w̃1 (v2 ) > w1 (0), which is a contradiction to the initial
assertion that v1 ≤ w1 (0).
Next, assume that v2 > w2 (0). Note that with v2 > w2 (0) and v1min = w1 (0), industry
3 cannot obtain a payoff that is better than free trade by making a proposal that will be
accepted by all industries. Hence, it must be that industry 3 proposes free trade when it
36
gets to be the proposer, and given that v1 ≤ w1 (0), industry 1 agrees to it. Given that
v1 ≤ w1 (0), industry 2 strictly prefers to form a coalition with industry 1. Industry 1, on
the other hand, would form a coalition with industry 2 if w̃1 (v2 ) > w1 (0), would randomize
between forming a coalition with 2 and proposing free trade if w̃1 (v2 ) = w1 (0), and would
propose free trade if w̃1 (v2 ) < w1 (0). So, the highest industry 2 can expect is v2 . Thus,
v2 ≤
n2
n1
n3
w̃2 (v1 ) + v2 + w2 (0).
N
N
N
Given that v1 ≤ w1 (0), w̃2 (v1 ) > w2 (0), so the above expression implies v2 < w̃2 (v1 ). Using
w̃i0 (v) < 0 and w̃1 (w̃2 (v)) = v, then, w̃1 (v2 ) > w̃1 (w̃2 (v1 )) = v1 . Given that v1 ≥ v1min =
w1 (0), we reach w̃1 (v2 ) > w1 (0). Thus,
v1 =
n1
n2
n3
w̃1 (v2 ) + v1 + w1 (0) ,
N
N
N
which implies that v1 > w1 (0). This again constitutes a contradiction. Hence, it must be
that v1 > w1 (0).
Proof of Lemma 4. Suppose on the contrary that FTA passes. Note that a coalition of
industries 1 and 2 will have enough seats to bypass presidential veto, whereas a coalition
between industries 1 and 3 or industries 2 and 3 is not veto-proof. Hence, industry 3 has
to either propose a bill that is unanimously agreed on, or propose free trade and get the
support of at least one of the other two industries. As in the proof of Lemma 3, all payoffs
in the following are evaluated in the limit as δ goes to 1 unless otherwise stated.
First assume that both industries 1 and 2 say yes to FTA (industry 3 may say yes or no;
it does not make a difference for what follows). This requires that both industries expect
a payoff that is not better than free trade in the bargaining subgame, i.e., v1 ≤ w1 (0)
and v2 ≤ w2 (0). Given that v1 ≤ w1 (0), industry 2 would always form a coalition with
industry 1 whenever it gets to make a proposal. This follows from the observation that
industry 2 can always make itself better off than free trade by proposing a tariff vector that
provides negative protection to industry 3 while providing free trade welfare to industry 1,
i.e., w̃2 (w1 (0)) > w2 (0), where w̃i is as defined in expression (11) in the proof of Lemma 3.
37
Given v1 ≤ w1 (0), this implies that w̃2 (v1 ) > w2 (0). The same reasoning is true for industry
1, too. That is, industry 1 would always form a coalition with industry 2 whenever it gets
to make a proposal. Industry 3, on the other hand, makes a proposal that will be accepted
by all members of Congress, because given that v1 ≤ w1 (0) and v2 ≤ w2 (0), industry 3 can
obtain a payoff that is at least as much as its free trade payoff. Hence,
v1 =
n1
(n2 + n3 )
w̃1 (v2 ) +
v1 ,
N
N
v2 =
n2
(n1 + n3 )
w̃2 (v1 ) +
v2 .
N
N
These expressions imply that v1 = w̃1 (v2 ) > w1 (0) and v2 = w̃1 (v1 ) > w2 (0), which is a
contradiction to the initial assertion that v1 ≤ w1 (0) and v2 ≤ w2 (0). Thus, both industries
1 and 2 cannot do worse than free trade in the bargaining subgame.
Next, assume v1 > w1 (0), v2 ≤ w2 (0) and v3 ≤ w3 (0), so that industries 2 and 3 say
yes to FTA. Under these conditions, industry 1 would again always form a coalition with
industry 2 whenever it gets to be the proposer in the bargaining subgame. Industry 2 may
choose to form a coalition with industry 1 if w̃2 (v1 ) ≥ w2 (0), or propose free trade and get
the support of industry 3. So, industry 2 can assure a payoff of w2 (0) at the minimum in
either case. Finally, industry 3 may make a proposal that will be accepted by all members
of Congress, or propose free trade and get the support of industry 2. First, suppose that
industry 3 makes a proposal that will be accepted by all industries. For a given δ,
v2 (δ) ≥
n2
(n1 + n3 )
w2 (0) +
[(1 − δ)w2 (τ s ) + δv2 (δ)] ,
N
N
which, after solving for v2 , becomes
v2 (δ) ≥
n2
(n1 + n3 )
w2 (0) +
(1 − δ)w2 (τ s ).
N − δ (n1 + n3 )
N − δ (n1 + n3 )
Similar to the proof of Lemma 3, denote the right-hand side of the above inequality as
v2min (δ). Note that lim v2min (δ) = w2 (0).
δ→1
Now, observe that with v1 > w1 (0) and v2min = w2 (0), industry 3 cannot obtain a payoff
that is better than free trade by making a proposal that will be accepted by all industries.
Hence, industry 3 proposes free trade when it is the proposer.
38
Given that industry 3 proposes free trade when it gets to be the proposer,
v1 =
n1
n2
n3
w̃1 (v2 ) + v1 + w1 (0) .
N
N
N
Since w̃1 (v2 ) > w1 (0), this expression implies that v1 < w̃1 (v2 ). As a result, w̃2 (v1 ) >
w̃2 (w̃1 (v2 )) = v2 . Since v2 ≥ v2min = w2 (0), it follows that w̃2 (v1 ) > w2 (0). In other words,
when industry 2 is the proposer, it chooses to form a coalition with industry 1 rather than
proposing free trade and obtaining the support of industry 3. Hence,
v2 =
n2
n1
n3
w̃2 (v1 ) + v2 + w2 (0) .
N
N
N
which implies v2 > w2 (0), so a contradiction.
The last scenario under which FTA would be granted is when v1 ≤ w1 (0), v2 > w2 (0)
and v3 ≤ w3 (0). This scenario is identical to the preceding scenario with the identities of
industries 1 and 2 switched. So, again, it will lead to a contradiction. As a result, in the
limit as δ → 1, both industries 1 and 2 must be doing strictly better than free trade in the
bargaining subgame, and therefore, both would say no to FTA in the first stage.
Proof of Lemma 5. In this case, similar to Case 1b, industries 2 and 3 have the option of
forming a coalition with each other and proposing free trade. However, now, in contrast to
Case 1b, industry 1 can form a veto-proof coalition with either of the other two industries,
so industry 2 will not have a strong bargaining position anymore. Here, we show that
both industries 2 and 3 do worse than free trade in the legislative bargaining subgame (i.e.,
vj ≤ wj (0) for j = 2, 3), so they vote in favor of FTA in the first stage. For convenience, all
payoffs are evaluated in the limit as δ → 1 in the remainder of the proof.
Suppose, on the contrary, that vj > wj (0) for j = 2, j = 3 or for both. Without any
loss of generality, assume v2 − w2 (0) ≥ v3 − w3 (0) (all of the following equally applies when
identities of 2 and 3 are switched). There are two possibilities to consider: v2 − w2 (0) ≥
v3 − w3 (0) > 0 and v2 − w2 (0) > 0 ≥ v3 − w3 (0).
First, suppose that v2 − w2 (0) ≥ v3 − w3 (0) > 0. This implies that v1 < w1 (0). This
3
P
is so since total surplus is maximized at free trade, implying that
(vi − wi (0)) ≤ 0. As
i=1
39
a result, industries 2 and 3 always form a coalition with industry 1 whenever they get to
make a proposal, because they can ensure a payoff in excess of free trade by doing so, i.e.,
w̃j6=1 (v1 ) > wj6=1 (0), where the function w̃j is as defined in expression (11) in the proof of
Lemma 3. Note that, by the symmetry of w̃i , w̃2 (v1 ) − w2 (0) = w̃3 (v1 ) − w3 (0). Industry 1
will have a strict preference for industry 3 as a coalition partner if v2 − w2 (0) > v3 − w3 (0),
and will randomize between the two if v2 − w2 (0) = v3 − w3 (0) (in which case w̃1 (v2 ) =
w̃1 (v3 )). In either case, we can write the proposer payoff of industry 1 as w̃1 (v3 ). Thus, the
continuation payoff of industry 1 can be expressed as
v1 =
n1
(n2 + n3 )
w̃1 (v3 ) +
v1 ,
N
N
which, after solving for v1 , becomes
v1 = w̃1 (v3 ).
In other words, as δ → 1, industry 1 obtains the same payoff in all possible outcomes of
the legislative bargaining. But, then, using the property w̃i (w̃j (v)) = v, it follows that
w̃3 (v1 ) = w̃3 (w̃1 (v3 )) = v3 . Given that industry 3 will be left out of the winning coalition
and obtain a payoff w321 < w3 (0) when industry 2 is the proposer, and will obtain at most
v3 when industry 1 is the proposer, we have the following
v3 ≤
n1
n2
n3
w̃3 (v1 ) + v3 + w321 .
N
N
N
Given that w̃3 (v1 ) = v3 , the above condition implies that v3 = w321 < w3 (0), which is a
contradiction to the initial assertion that we made.
The second possible scenario is v2 − w2 (0) > 0 ≥ v3 − w3 (0). In this case, industry 1 will
have a strict preference for industry 3 as a coalition partner. First, suppose w̃2 (v1 )−w2 (0) =
w̃3 (v1 )−w3 (0) > 0 so that both industries 2 and 3 choose to form a coalition with industry 1
whenever they get to make a proposal. Following the same steps as in the previous scenario,
it is easy to reach v1 = w̃1 (v3 ) and w̃3 (v1 ) = v3 . The continuation payoff of industry 2 can
be written as
v2 =
n1
n3
n2
w̃2 (v1 ) + w213 + w231 .
N
N
N
40
Given that w̃2 (v1 ) − w2 (0) = w̃3 (v1 ) − w3 (0) and that w̃3 (v1 ) = v3 , we have
v2 =
n2
n1
n3
(w2 (0) + v3 − w3 (0)) + w213 + w231 .
N
N
N
Since v3 − w3 (0) ≤ 0 by assumption and also w213 < w2 (0) and w231 < w2 (0), it follows
that v2 < w2 (0), which is a contradiction. Next, suppose that w̃2 (v1 ) − w2 (0) = w̃3 (v1 ) −
w3 (0) ≤ 0. In this case, industry 2 will obtain a payoff of w2 (0) when it is the proposer
(it will randomize between forming a coalition with industry 1 and proposing free trade if
w̃2 (v1 ) = w2 (0); otherwise, it will propose free trade and industry 3 will say yes). Industry
3, on the other hand, will always form a coalition with industry 1 (because, given that
v2 > w2 (0), industry 2 would not agree to free trade). Hence, v2 can be expressed as
v2 =
n2
n1
n3
w2 (0) + w213 + w231 .
N
N
N
Since w213 < w2 (0) and w231 < w2 (0), it follows that v2 < w2 (0), so again a contradiction.
Hence, vj ≤ wj (0) for j = 2, 3, and therefore both industries 2 and 3 vote in favor of FTA
in the first stage.
Proof of Proposition 3. Recall that Q1 + Q2 + Q3 = θ. Given that the industries are
symmetrically dispersed, the legislative bargaining has a full randomization SSPE. Hence,
the continuation per-capita payoff of districts that produce good i is the same as in equation
(9) (which is given in the proof of Proposition 1)
θ
1
vi = wi (0) + θ( − Qi ) −
3
2
X
5 2
θ −
Q2l
9
l=i,j,k
!
.
There are couple of observations to make here. First, from equation (12),
(12)
3
P
(vi − wi (0)) ≤ 0
i=1
since total surplus is maximized at free trade. As a result, if FTA is given to the President,
she will always choose free trade since for each industry, free trade is not worse than any
symmetric status quo tariff vector (τ = τ s ) that would continue to prevail in case the
President’s proposal is rejected. Second, given our assumption that Q1 > Q2 > Q3 , as
long as we determine the range in which v2 − w2 (0) > 0, this will automatically imply
41
v3 − w3 (0) > 0 and hence FTA will not be given. This is true since each district’s payoff is
decreasing in its own industry’s total output and increasing in other industries’ total output.
Therefore, if industry 2 does better than free trade, then industry 3, which has a lower
output than industry 2, will do better than free trade, too. In addition, industry 1 cannot
be made better off than free trade and therefore always votes yes to FTA.33
To analyze the possible cases in detail, let’s rewrite Q1 as Q1 = θ − Q2 − Q3 . If we
substitute this value in equation (12) and solve for a critical value of Q3 , Q3 , as a function
of Q2 that makes v2 − w2 (0) = 0, we get
1
Q3 = (θ − Q2 ) −
2
We can see from equation (13) that
dQ3
dQ2
p
54θQ2 − 11θ2 − 27Q22
.
6
(13)
< 0. In addition, we know that 0 ≤ Q3 ≤ Q2 .
Using these conditions in equation (13), we can determine the region where FTA is given
and where it is not given.
Case 2a: Q2 > 3θ ; nN1 =
n2
N
=
n3
N
= 13 ; τ1s = τ2s = τ3s
It is possible to show that, when Q2 > 3θ , industries 1 and 2 cannot do better than free
trade and hence FTA will be granted.34 Since each industry’s payoff is decreasing in its own
output, we need to find the upper bound of Q2 that satisfies equation (13). This gives us
the maximum amount of Q2 that makes industry 2 indifferent between granting FTA or not
granting FTA. Above that level, it is not possible for industry 2 to do better than free trade,
thus FTA will be granted. Since
dQ3
dQ2
< 0, we can find the upper bound of Q2 by setting
Q3 equal to zero in equation (13), which gives us Q2 = 3θ . From equation (13), any Q2 >
θ
3
requires Q3 < 0 for industry 2 to do strictly better than free trade by not granting FTA,
which is not possible.
33
This is easy to see since the best possible scenario for industry 1 (given that Q1 > Q2 > Q3 ) is the one
where Q1 = Q2 = Q3 and this corresponds to fully symmetric case where each industry prefers free trade to
the bargaining subgame.
34
Given our assumption that Q1 > Q2 > Q3 , under this case, industries 1 and 2 cannot do better than
free trade for sure. On the other hand, depending on the value of Q3 , industry 3 can do better or worse than
free trade.
42
Case 2b: Q2 <
θ
2
1−
√ √7
; nN1
3 3
=
n2
N
=
n3
N
= 13 ; τ1s = τ2s = τ3s
It is possible to show that, when Q2 <
θ
2
1−
√ √7 ,
3 3
industries 2 and 3 do better than
free trade and as a result FTA will not be granted. Since each industry’s payoff is decreasing
in its own total output, we need to find the lower bound of Q2 that satisfies equation (13).
This gives us the minimum amount of Q2 that makes industry 2 indifferent between granting
FTA and not granting FTA. Below that level, it is always possible for industry 2 to do better
dQ3
dQ2
< 0 and Q3 ≤ Q2 , we can find the
√ lower bound of Q2 by setting Q2 = Q3 in equation (13), which gives us Q2 = 2θ 1 − 3√73 .
√ b where the value of
From equation (13), any Q2 < 2θ 1 − 3√73 requires a value of Q3 ≤ Q,
than free trade, thus FTA will not be granted. Since
b is such that Q2 < Q,
b for industry 2 to benefit from not granting FTA, which is always
Q
satisfied since Q3 ≤ Q2 .
Case 2c:
θ
2
1−
√ √7
3 3
≤ Q2 < 3θ ; nN1 =
n2
N
=
n3
N
= 31 ; τ1s = τ2s = τ3s
In this case, we again use equation (13). For any value of Q2 such that
θ
2
1−
√ √7
3 3
≤
Q2 < 3θ , if Q3 < Q3 , industries 2 and 3 do better than free trade and FTA is not given. This
is true since
dQ3
dQ2
< 0 and each industry’s payoff is decreasing in its own output. As a result,
a value of Q3 < Q3 , for a given value of Q2 , results in a strictly higher welfare for industry 2
when FTA is not granted. On the other hand, if Q3 > Q3 , then industry 2 cannot be made
better off than free trade and FTA will be given (recall that industry 1 always votes YES to
FTA).35
Proof of Proposition 4. In the first part of the proof, we will assume that FTA is always
granted to the President and analyze the President’s problem accordingly. In the second
part, we show that all three industries are better off under FTA relative to the bargaining
subgame, hence FTA is always granted.
Given Assumption 1, we have
2θ
θ
− ≤ τis ≤ .
3
3
35
In this case, industry 3 can do better or worse than free trade depending on the value of Q3 .
43
Using equation (5), each district’s expected welfare is given by
"
2 2 !#
X
1
θ
θ
wi − wi (τ s ) = θ(τi − τis ) −
τl +
− τls +
.
2 l=i,j,k
3
3
Moreover, using equation (6), we can also write each district’s welfare as
2 2 !
1 X
θ
θ
wi − wi (0) = θτi −
τl +
−
.
2 l=i,j,k
3
3
Then, by subtracting the former equation from the latter, we get
s
wi (τ ) − wi (0) =
θτis
X (τ s )2
θ X s
l
−
τ −
.
3 l=i,j,k l l=i,j,k 2
There are a couple of things to note here. First,
3
P
(wi (τ s )−wi (0)) ≤ 0 since max
i=1
3
P
(14)
τ
3
P
wi (τ ) =
i=1
wi (0). Therefore, there is at least one industry that will be worse off under any status quo
i=1
relative to free trade (except if the status quo is free trade). Second, given our assumption
that τ1s > τ2s > τ3s , and since each industry’s payoff is increasing in its own protection and
decreasing in other industries’ protection, if w2 (τ s )−w2 (0) > 0, this will automatically imply
that w1 (τ s ) − w1 (0) > 0. As a result, the status quo payoffs of industries 1 and 2 will be
strictly higher than their payoffs under free trade and thus the President cannot choose free
trade under FTA. In addition, industry 3 cannot be better off than free trade and therefore
always prefers free trade. To analyze Case 3 in detail, we write equation (14) for industry 2,
s
w2 (τ ) − w2 (0) =
θτ2s
X (τ s )2
θ X s
l
−
τl −
.
3 l=i,j,k
2
l=i,j,k
(15)
In addition, we rewrite the President’s welfare function given in equation (3) by using
equation (6) as
"
2 2 !#
X
X
θ
1
θ
θ
τl −
τl +
−
.
W = W (0) +
3 l=i,j,k
2 l=i,j,k
3
3
Note that whenever w2 (τ s ) − w2 (0) ≤ 0, the President can do unconstrained maximization
under FTA and choose free trade (since both industry 2 and industry 3 are better off under
44
free trade compared to the status quo). On the other hand, if w2 (τ s )−w2 (0) > 0, then under
FTA, the President needs to offer a tariff vector that makes the pivotal industry (industry
2) indifferent with respect to the status quo. As a result, by using equation (15), we can
state the President’s constraint as
w2 (τ P ) − w2 (0) > w2 (τ s ) − w2 (0)
OR
θτ2P
X τlP
θ X P
−
τl −
3 l=i,j,k
2
l=i,j,k
2
> w2 (τ s ) − w2 (0),
where τ P = (τ1P , τ2P , τ3P ) represents the tariff vector the President chooses under FTA. The
maximization problem the President faces is then given by
"
P P 1 P P θ 2
max W (0) + 3θ
τl − 2
τl + 3 −
τP
l=i,j,k
l=i,j,k
"
+ µ θτ2P −
θ
3
P
τlP −
l=i,j,k
P (τlP )2
l=i,j,k
2
θ 2
#
3
#
− (w2 (τ s ) − w2 (0)) .
It is easy to show that when w2 (τ s ) − w2 (0) < 0, the constraint is not binding (so
µ = 0) and τ P = (0, 0, 0), i.e., free trade. On the other hand, when w2 (τ s ) − w2 (0) > 0,
the constraint binds (so µ > 0). Then, first order conditions imply that τ1P = τ3P = −
τ2P
2
.
Putting these back into the constraint gives us
p
τ1P = τ3P = − 13 θ − θ2 − 3 (w2 (τ s ) − w2 (0)) < 0
(16)
τ2P
=
2
3
p
θ − θ2 − 3 (w2 (τ s ) − w2 (0)) > 0.
Notice that when w2 (τ s ) − w2 (0) = 0, we still have τ P = (0, 0, 0), i.e., free trade. Hence, we
can conclude that whenever w2 (τ s ) − w2 (0) > 0, the tariff vector the President chooses is
different than free trade, i.e., τ P 6= (0, 0, 0). On the other hand, when w2 (τ s ) − w2 (0) ≤ 0,
the President always chooses free trade.
In addition to the above analysis, it is also possible to determine the boundary of the
region where free trade is chosen by the President under FTA, which is the same as the set
45
of status quo tariffs such that w2 (τ s ) = w2 (0). This condition yields
q
θ2 + 12θτ2s − 6θτ1s − 9 (τ1s )2 − 9 (τ2s )2 θ
s
− .
τ3 ≡
3
3
(17)
Equation (17) defines a surface in the three-dimensional space of tariff vectors, for τ2s ∈
(− 3θ , 2θ
) and τ1s ∈ (τ2s , 2θ
). Any point on this surface is a point for which industry 2 is
3
3
indifferent between the status quo and free trade. If we begin on the surface and reduce τ1s
or τ3s or increase τ2s , industry 2 will now strictly prefer the status quo to free trade, and the
President will not propose free trade. If we perturb the tariff vector in the opposite direction,
industry 2 will strictly prefer free trade, and free trade will be the equilibrium result.
We can see from equation (17) that
dτ s3
dτ2s
> 0 and
dτ s3
dτ1s
≤ 0. In addition, we know that
τ3s ≤ τ2s ≤ τ1s . Using these conditions in equation (17), under FTA we can determine the
region where the President chooses free trade and where she does not.
√
Case 3a:
τ2s
>
(1+ 3)θ
6
√
or
τ2s
<
(1− 3)θ
6
;
n1
N
It is possible to show that, when τ2s >
n2
= nN3 = 31 ; Q1 = Q2 = Q3 = 3θ
N
√
√
(1+ 3)θ
(1− 3)θ
s
or
τ
<
, industries
2
6
6
=
2 and 3 do
worse than free trade and hence once FTA is given to the President, she will choose free
trade and it will be approved by Congress with the support of industries 2 and 3.36 We need
to find the bounds of τ2s that satisfy equation (17). This gives us the values of τ2s that make
industry 2’s payoff equal under the status quo and free trade. Above that level, it is not
possible for industry 2 to do better than free trade (since that requires τ s3 < − 3θ , which is not
possible by Assumption 1) thus free trade will result once FTA is granted to the President.
Since each industry’s payoff is increasing in its own status quo tariff and decreasing in other
industries’ status quo tariffs, we can find the bounds of τ2s that satisfy equation (17) by
setting τ1s = τ2s and τ3s = − 3θ (its lower bound) and solving for τ2s , which gives us
√ 1+ 3 θ
s
s
and
τ1 = τ2 =
6√ 1− 3 θ
τ1s = τ2s =
.
6
36
Given our assumption that τ1s > τ2s > τ3s , under this case, industries 2 and 3 will do worse than free
trade for sure. On the other hand, industry 1 can do better or worse than free trade depending on the value
of τ1s .
46
√
(1+ 3)θ
Given that τ1s > τ2s , for any value of τ2s >
6
√
or τ2s <
(1− 3)θ
6
, we will have w2 (τ s ) −
w2 (0) < 0. Therefore, once FTA is given, free trade will be chosen by the President.
√
Case 3b:
(1− 3)θ
6
√
≤ τ2s ≤
(1+ 3)θ
6
;
n1
N
=
n2
N
=
n3
N
= 31 ; Q1 = Q2 = Q3 =
√
√
In this case, for any value of
τ2s
such that
(1− 3)θ
6
θ
3
≤
τ2s
≤
(1+ 3)θ
6
, we can find a critical
value of τ3s , say τ s3 , that satisfies equation (17). Then, if τ3s < τ s3 , industries 1 and 2 do better
than free trade and under FTA, the President has to offer a tariff vector τ P 6= (0, 0, 0) given
in equation (16) that makes the pivotal industry (industry 2) indifferent to the status quo.
At the same time, this tariff vector makes industry 3 better off whereas industry 1 worse off
compared to the status quo. On the other hand, if τ3s > τ s3 , industries 2 and 3 cannot do
better than free trade and under FTA, the President chooses free trade, τ P = (0, 0, 0).
So far, we have assumed that FTA is always given to the President. In this part, we
show it is indeed the case that granting FTA to the President is optimal for all industries.
To do so, we will compare each industry’s payoff under FTA and under no FTA and show
that the payoffs under FTA are strictly better than the payoffs under no FTA.
Under FTA, since the President has to keep industry 2 as well off as it would be under
the status quo, the payoffs industry 1 and industry 3 obtain are strictly decreasing in the
status quo payoff of industry 2. Given that w2 (τ ) is decreasing in τ1 and τ3 and increasing
in τ2 , and given our ordering τ1s > τ2s > τ3s , the vector of status quo tariffs that maximize
w2 (τ s ) necessarily implies τ1s = τ2s . Hence, using equation (15), the maximization problem
can be written as
s
max
w2 (τ ) = w2 (0) +
s
τ
θτ2s
X (τ s )2
θ X s
l
−
τl −
s.t. τ1s = τ2s ,
3 l=i,j,k
2
l=i,j,k
leads to the vector of status quo tariffs
θ
τ1s = τ2s = ,
6
θ
τ3s = − .
3
47
The value of w2 (τ s ) evaluated at these tariffs is,
w2 (τ s ) = w2 (0) +
θ2
.
12
(18)
Given τ1s > τ2s > τ3s , this is the highest payoff industry 2 can obtain under the status quo.
By equation (16), when τ s = 6θ , 6θ , − 3θ , the President chooses
!
r
2
1
3θ
τ1P = τ3P = −
θ−
,
3
4
!
r
2
3θ2
P
τ2 =
θ−
.
3
4
Plugging these back into equation (6), we have


!
!2
r
r
2
2
2
2
θ
3θ
1
2 3θ
2 3θ
θ
w3 = w3 (0) −
θ−
−  θ−
+
− 
3
4
2
3
4
9
4
3
r
r
2 !
2
θ2 θ 3θ2 1
4θ
3θ
2
3θ
= w3 (0) −
+
−
θ2 −
+
3
3
4
2
3
4
9
4
r !
11
3
−
.
= w3 (0) − θ2
12
4
Since τ1P = τ3P , we have w1 = w3 under FTA. Notice that this is the lowest payoff industries 1
and 3 can get. If we compare this payoff with the one under the bargaining subgame given in
q 3
equation (10), we can see that it is larger since the second term in the last line, θ2 11
,
−
12
4
is less than
θ2
.
9
Moreover, we know that industry 2’s payoff under FTA is bounded below by
what it obtains under free trade, thus industry 2 does always better under FTA relative to
the bargaining subgame. As a result, all three industries obtain strictly higher payoffs under
FTA than what they would obtain in the bargaining subgame, and therefore FTA is granted
in the first stage to the President.
References
[1] Baron, D.P., 1993. A theory of collective choice for government programs. Mimeo, Stanford University.
48
[2] Baron, D.P. and J.A. Ferejohn, 1989. Bargaining in legislatures. American Political
Science Review 83, pp. 1181-1206.
[3] Baron, D.P. and E. Kalai, 1993. The simplest equilibrium of a majority-rule division
game. Journal of Economic Theory 61, pp. 290-301.
[4] Celik, L. and B. Karabay, 2011. A note on equilibrium uniqueness in the Baron-Ferejohn
model. Working Paper, CERGE-EI and University of Auckland, May. Available at
SSRN: (http://ssrn.com/abstract=1718719).
[5] Celik, L., B. Karabay, and J. McLaren, 2011. Trade policy making in a model of legislative bargaining. NBER Working Paper No. 17262 (July).
[6] Conconi, P., G. Facchini and M. Zanardi, (forthcoming). Fast track authority and international trade negotiations. American Economic Journal: Economic Policy.
[7] Destler, I.M. 1991. U.S. trade policy-making in the Eighties. In Alberto Alesina and
Geoffrey Carliner (eds.), Politics and Economics in the Eighties, Chicago: University of
Chicago Press, pp. 251-84.
[8] Eraslan, H., 2002. Uniqueness of stationary equilibrium payoffs in the Baron-Ferejohn
model. Journal of Economic Theory 103, pp. 11-30.
[9] Gagnon, J.E., 2003. Long-run supply effects and the elasticities approach to trade.
International Finance Discussion Papers No. 754, Board of Governors of the Federal
Reserve System (January).
[10] Koh, H.H., 1992. The fast track and United States trade policy. Brooklyn Journal of
International Law 18, pp. 143-180.
[11] Li, D., 2009. Multiplicity of equilibrium payoffs in three-player Baron-Ferejohn model.
Working paper, Chinese University of Hong Kong.
49
[12] Lohmann, S. and S. O’Halloran, 1994. Divided government and U.S. trade policy: theory
and evidence. International Organization 48, pp. 595-632.
[13] Marquez, J., 1990. Bilateral trade elasticities. Review of Economics and Statistics 72,
pp. 70–77.
[14] McLaren, J. and B. Karabay, 2004. Trade policy making by an assembly. In: D. Mitra
and A. Panagariya (eds.), The Political Economy of Trade, Aid and Foreign Investment
Policies: Essays in Honor of Edward Tower, Amsterdam: Elsevier.
[15] Primo, D.M., 2006. Stop us before we spend again: institutional constraints on government spending. Economics and Politics 18, pp. 269-312.
[16] Riker, W.H., 1962. The Theory of Political Coalitions. New Haven: Yale University
Press.
[17] Smith, C.C., 2006. Trade promotion authority and fast-track negotiating authority for
trade agreements: major votes. CRS Report RS21004, Congressional Research Service
(October).
50
Congress
> 1/2 vote
FTA
No FTA
Legislatori
President
τp
τi
Congress
> 1/2 vote
Pass
τp
Congress
> 1/2 vote
Pass
Fail
τs
Fail
Presidential veto
Pass
τi
Legislator
τj
Fail
Legislator
Congress
> 1/2 vote
.
.
.
i
τi
Congress
2/3 vote
Pass
τi
Fail
Legislator
k
τk
Congress
> 1/2 vote
.
.
.
Figure 1. Timing of the Trade Policy Formation Game
j
Q3 = Q2
Q3
54θQ2 − 11θ 2 − 27Q22
1
Q3 (Q2 ) = (θ − Q2 ) −
2
6
No FTA
region
450
θ 
1−
2 3
7  θ
3 3
Q2
Figure 2. Asymmetric Industry Outputs
τ 3s
τ3s =τ2s
450
τ 2s
τP = 0
•
A
τP ≠ 0
−
θ
(1− 3)θ
3
6
τ 1s = 0.3θ
(1+ 3)θ
6
θ 2 +12τ 2s − 9(τ 2s ) − 6θτ1s − 9(τ1s )
2
s
3
s
1
s
2
τ (τ ,τ ) =
2θ
3
3
Figure 3. Asymmetric Status quo Tariffs
2
−
θ
3